(FGV/2020) Dez pessoas, entre elas Gilberto e Laura, pretendem formar uma comissão com quatro membros escolhidos entre os dez. Quantas comissões são possíveis se Gilberto e Laura podem ou não comparecer, mas nunca juntos na mesma comissão? A) 182 B) 45 C) 240 D) 100 E) 70
RESOLUÇÃO: Desse universo de 10 pessoas, o total de comissões que podem ser formadas, com 4 pessoas é dado por uma C10,4. Então: C10,4 = 10!/ 4!6! C10,4 = 10.9.8.7.6!/ 4.3.2.1.6! Simplificando 6! com 6!, tem-se: C10,4 = 5040/ 24 C10,4 = 210 comissões O total de comissões com Gilberto e Laura juntos é dado por C8,2 Então: C8,2 = 8! / 6!2! C8,2 = 28 comissões O total de comissões que Gilberto e Laura podem ou não comparecer, mas, nunca juntos é 210 – 28 = 182 Resp.: A VEJA TAMBÉM: |
Dado um conjunto de 10 pessoas quantas comissões diferentes de 3 pessoas e possível formar
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