A team of $6$ people is to be chosen from a group consisting of $12$ adults and $4$ children t

Question

A team of $6$ people is to be chosen from a group consisting of $12$ adults and $4$ children to form a choir group. In how many ways can the team be chosen without restriction?[1] In how many ways can the team be chosen if it must contain at least $2$ adults and at least $1$ child?[2] The $12$ adults consist of $5$ men and $7$ women. In how many ways can $2$ particular women of the $7$ are grouped together and no two men are next to each other.[3]

Accepted Answer

(a) 8008. (b) 7084. (c) 3628800, under the source-intended interpretation of arranging all 12 adults in a line.

2024 SAJC H1 Q6

2024 SAJC H1 Q6

Solution:

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