Premutations

Question

An employer interviews 9 people for 4 technical support positions in a company, and 5 of the 9 people are women. If all 9 are qualified, in how many ways can the employer fill the technical support positions if exactly 2 are women

Answer 1

1. The problem is stating to determine how many ways there are to fill the 4 technical support positions with exactly 2 woman and 2 men
2. This is really a problem in combinations, not permutations, because order does not matter.
3. First, how many combinations are there in picking 2 of 5 woman.  We use the terminology nCr, which means we have n things and want to know how many ways there are to pick r of them.  And nCr = n! / (n-k)!(k)!
1. Pick 2 out of 5 woman.  5C2 = 5! / (5-2)! 2! =  5!/(3!* 2!) = 10
2. Pick 2 out of 4 men.  4C2 = 4! / (4-2)! 2! = 4!/(2! * 2!) = 6
4. To find the total number of combinations, multiply the two numbers together :   10*6 = 60 .