SOLUTION: A company has six female and eight male employees.How many different 5-person committees can be formed, if the committee must have a group leader and the members at large must cons

Algebra ->  Permutations -> SOLUTION: A company has six female and eight male employees.How many different 5-person committees can be formed, if the committee must have a group leader and the members at large must cons      Log On


   

Question 645233: A company has six female and eight male employees.How many different 5-person committees can be formed, if the committee must have a group leader and the members at large must consist of two women and two men?
Answer by stanbon(75887) About Me  (Show Source):
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A company has six female and eight male employees.How many different 5-person committees can be formed, if the committee must have a group leader and the members at large must consist of two women and two men?
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# of ways to pick 2 women: 6C2 = 15
# of ways to pick 2 men: 8C2 = 28
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# of ways to then pick a group leader: 10
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# of 5-person committees with 2 men and 2 women and a group leader
= 15*28*10
= 4200 ways
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Cheers,
Stan H.