assume the president must choose from a pool of 25 candidates consisting of 15 m

Question

assume the president must choose from a pool of 25 candidates consisting of 15 men and 10 women.

A) how many ways are there of filling all the positions of his cabinet if we assume that each position be filled by a different person and take into account which position each been has been assigned?

B) how many ways are there of filling all the positions of his cabinet if we assume that each position be filled by a different person and do not take into account which position each been has been assigned?

C) assuming part (b) how many ways are there of filling the cabinet with 8 men and 7 women?

Explanation / Answer

Number of ways in which he can choose his cabinet = 25P15=4,274,473,667,143,680,000

Number of ways in which he can choose his cabinet = 25C15=3,268,720

C) Total Number of ways = Number of ways in which men acan be selected * Number of ways in whichi women can be selcted = 15C8*10C7= 772,000

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