A department needs to choose six members consists of 3 women and 3 men from 10 men and 15 women. The number of ways it can be selected is 54,600.
If r persons need to be selected from total n members and the order does not matter, the number of ways it can be selected is calculated using the combination formula:
ⁿCr = n! / [(n-r)! r!]
Data from the problem:
Total man = 10
Man to be chosen = 3
Total woman = 15
Woman to be chosen = 3
Hence,
The number of ways men can be selected = ¹⁰C₃ = 10! /(3! 7!)
= 120
The number of ways women can be selected = ¹⁵C₃ = 15! /(3! 12!)
= 455
The number of ways men and women selected:
= ¹⁰C₃ x ¹⁵C₃
= 120 x 455 = 54,600 ways
Hence, the number of ways the members can be selected = 54,600 ways.
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