Análise combinatória
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Análise combinatória
(Insper 2012) Em cada ingresso vendido para um show de música, é impresso o número da mesa onde o comprador deverá se sentar. Cada mesa possui seis lugares, dispostos conforme o esquema a seguir.
![Análise combinatória 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)
b) 120.
c) 192.
d) 384.
e) 720.
A correta é a letra C.
O lugar da mesa em que cada comprador se sentará não vem especificado no ingresso, devendo os seis ocupantes entrar em acordo. Os ingressos para uma dessas mesas foram adquiridos por um casal de namorados e quatro membros de uma mesma família.
Eles acordaram que os namorados poderiam sentar-se um ao lado do outro. Nessas condições, o número de maneiras distintas em que as seis pessoas poderão ocupar os lugares da mesa é
a) 96.b) 120.
c) 192.
d) 384.
e) 720.
A correta é a letra C.
siriusbk- Padawan
- Mensagens : 97
Data de inscrição : 30/12/2022
Localização : Patos, paraíba
Re: Análise combinatória
Sejam A e B o casam de namorados
Existem n' = 8 possibilidades deles sentarem:
1) No alto ---> AB _ , BA _ , _ AB , _ BA
3) Em baixo -> AB _ , BA _ , _ AB , _ BA
Para cada uma das 8 possibilidades a família deverá ocupar os lugares restantes:
n" = A(4, 4) = 24
n = n'.n" ---> n = 8.24 ---> n = 192
Existem n' = 8 possibilidades deles sentarem:
1) No alto ---> AB _ , BA _ , _ AB , _ BA
3) Em baixo -> AB _ , BA _ , _ AB , _ BA
Para cada uma das 8 possibilidades a família deverá ocupar os lugares restantes:
n" = A(4, 4) = 24
n = n'.n" ---> n = 8.24 ---> n = 192
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