técnicas de contagem
DESCRIPTION
Técnicas de Contagem. Quantos números de três algarismos distintos podemos formarempregando os caracteres 1, 3, 5 e 9 ?. 1. 1. 1. 1. 1. 1. 6. 1. 3. 3. 5. 5. 9. 9. =. 3. 5. 9. 9. 5. 3. 3. 3. 3. 3. 3. 3. 6. 3. 1. 1. =. 5. 5. 9. 9. 1. 1. 9. 5. 5. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/1.jpg)
Técnicas
de
Contagem
![Page 2: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/2.jpg)
Quantos números de três algarismos distintos podemos formarempregando os caracteres 1, 3, 5 e 9 ?
![Page 3: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/3.jpg)
1
3
5
9
1
3
5
1
3
9
1
5
3
1
5
9
1
9
5
1
9
3
3
5
9
3
5
1
3
9
1
3
9
5
3
1
5
3
1
9
5
9
1
5
9
3
5
1
3
5
1
9
5
3
9
5
3
1
9
1
3
9
1
5
9
3
5
9
3
1
9
5
1
9
5
3
= 6
= 6
= 6
= 6
24TOTAL
![Page 4: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/4.jpg)
Com os caracteres 1, 3, 5 e 9 podemos formar 24 algarismos distintos!
![Page 5: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/5.jpg)
Há 4 meios de
transporte entre as
cidades A e B
![Page 6: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/6.jpg)
Cidade A
Cidade B1
º2º3º4º
![Page 7: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/7.jpg)
E três meios de transporte entre B e C
![Page 8: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/8.jpg)
Cidade B
Cidade C
1º
2º
3º
![Page 9: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/9.jpg)
Calcule o numero de modos de fazer o percurso de A até C passando por B
![Page 10: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/10.jpg)
Modos
123
+++
![Page 11: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/11.jpg)
456
+++
![Page 12: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/12.jpg)
7
89
+++
![Page 13: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/13.jpg)
101112
+++
![Page 14: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/14.jpg)
Concluímos, portanto que podemos calcular 12 maneiras diferentes de ir da cidade A até a cidade C, passando pela B
![Page 15: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/15.jpg)
Um vagão de trem possui 7 portas. De quantas maneiras distintas um passageiro pode entrar no trem e sair dele por uma porta diferente da que entrou?
![Page 16: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/16.jpg)
Entrar
1Sair
23456
![Page 17: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/17.jpg)
789101112
![Page 18: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/18.jpg)
131415161718
![Page 19: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/19.jpg)
192021222324
![Page 20: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/20.jpg)
252627282930
![Page 21: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/21.jpg)
313233343536
![Page 22: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/22.jpg)
373839404142
![Page 23: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/23.jpg)
Então, teremos 42 maneiras diferentes de entrar e sair do trem por portas diferentes
![Page 24: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/24.jpg)
Numa festa há 7 moças e 5 rapazes, quantos casais podem ser formados?
![Page 25: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/25.jpg)
Moças
![Page 26: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/26.jpg)
Rapazes
![Page 27: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/27.jpg)
Casais
![Page 28: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/28.jpg)
![Page 29: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/29.jpg)
![Page 30: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/30.jpg)
![Page 31: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/31.jpg)
![Page 32: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/32.jpg)
Poderá ser formado 35 casais
![Page 33: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/33.jpg)
Um artista tem 3 cartolas, 4 casacos e 2 bengalas, todos diferentes. Quantas apresentações ele pode fazer sem repetir as três mesmas peças?
![Page 34: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/34.jpg)
3 cartolas
2 bengalas
4 casacos
![Page 35: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/35.jpg)
1
2
![Page 36: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/36.jpg)
3
4
![Page 37: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/37.jpg)
5
6
![Page 38: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/38.jpg)
7
8
![Page 39: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/39.jpg)
9
10
![Page 40: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/40.jpg)
1112
![Page 41: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/41.jpg)
1314
![Page 42: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/42.jpg)
15
16
![Page 43: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/43.jpg)
1718
![Page 44: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/44.jpg)
1920
![Page 45: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/45.jpg)
2122
![Page 46: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/46.jpg)
23
24
![Page 47: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/47.jpg)
Então, será possível formar 24 conjuntos diferentes com 3 cartolas, 4 casacos e 2 bengalas
![Page 48: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/48.jpg)
Quantos são os anagramas da palavra “PATO”. Escreva 6 deles
![Page 49: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/49.jpg)
PatoAPTOTOPAATOPOPATTAPOOPTA
1 2 3 4
1
2
3
4
5
6
6 x 4 = 24
![Page 50: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/50.jpg)
Uma moeda é lançado 4 vezes. Qual o numero de seqüências possíveis de cara e coroa
![Page 51: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/51.jpg)
Cara
Coroa
![Page 52: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/52.jpg)
![Page 53: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/53.jpg)
![Page 54: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/54.jpg)
![Page 55: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/55.jpg)
A moeda lançada 4 vezes tem 16 sequências possíveis de dar cara e coroa
![Page 56: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/56.jpg)
Com 4 pontos distintos num plano, não tendo mais do que dois na mesma reta, quantas retas podemos traçar por esses quatro pontos
![Page 57: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/57.jpg)
Podemos traçar 6 retas ligando os 4 pontos num plano
![Page 58: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/58.jpg)
Com 4 pontos distintos num plano, não tendo mais do que dois na mesma reta, quantas retas podemos traçar por esses quatro pontos
![Page 59: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/59.jpg)
12
34
Podemos formar 4 triângulos ligando os 4 pontos num plano
![Page 60: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/60.jpg)
Uma determinada viagem pode ser feita de avião,
ônibus, caminhão ou carro.
![Page 61: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/61.jpg)
De quantos modos pode-se escolher um meio de
transporte se não for usado na volta o mesmo
da ida?
![Page 62: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/62.jpg)
1
2
3
![Page 63: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/63.jpg)
4
5
6
![Page 64: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/64.jpg)
7
8
9
![Page 65: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/65.jpg)
10
11
12
![Page 66: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/66.jpg)
Podemos escolher 12 formas de ir e voltar sem usar o mesmo meio de
transporte.
![Page 67: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/67.jpg)
Deseja-se pintar uma bandeira, com 3 faixas
verticais, dispondo 3 cores, sem que se tenha duas faixas consecutivas da mesma cor. De quantas
maneiras isso é possível?
![Page 68: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/68.jpg)
Cores
![Page 69: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/69.jpg)
![Page 70: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/70.jpg)
![Page 71: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/71.jpg)
É possível formar 12 bandeiras diferentes com
as 3 cores
![Page 72: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/72.jpg)
Um torneio de Vôlei é disputado por 4 seleções:Brasil,Canadá,Cuba e EUA. De quantas maneiras distintas podemos ter os três primeiros colocados(1º,2º e 3º).
![Page 73: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/73.jpg)
1
23456
7
89
101112
![Page 74: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/74.jpg)
13
1415161718
19
2021222324
![Page 75: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/75.jpg)
Temos 24 maneiras de ter o 3 primeiros colocados!
![Page 76: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/76.jpg)
Um restaurante oferece no cardápio 2 tipos pratos de entrada e 4 tipos de saladas. De quantas maneiras distintas uma pessoa pode fazer o seu pedido, contendo um prato de entrada e um tipo de salada?
![Page 77: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/77.jpg)
Entrada Salada
![Page 78: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/78.jpg)
1
2
3
4
![Page 79: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/79.jpg)
5
6
7
8
![Page 80: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/80.jpg)
Podemos formar 8 combinações diferentes com 2 tipos de
entrada e 4 tipos de salada.
![Page 81: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/81.jpg)
Numa urna estão 4 bolas de cores diferentes
![Page 82: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/82.jpg)
1
2
3 6
5
4
![Page 83: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/83.jpg)
7
8
9 12
11
10
![Page 84: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/84.jpg)
Temos 12 maneiras diferentes de retirar as bolinhas sem que se
repita a cor.
![Page 85: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/85.jpg)
Quantas diagonais há em um quadrado?
![Page 86: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/86.jpg)
1
![Page 87: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/87.jpg)
2
![Page 88: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/88.jpg)
Em um quadrado há 2 diagonais
![Page 89: Técnicas de Contagem](https://reader038.vdocuments.pub/reader038/viewer/2022103006/568139fc550346895da1c102/html5/thumbnails/89.jpg)
Luciano - Nº 25, Deric Nº 7 – 2º B
ETEC “João Gomes de Araújo”
Professor: Camilo