An employer interviews 10 people for 5 technical support positions in a company, and 5 of the 10 people are men. if all 10 are qualified, in how many ways can the employer fill the technical support positions if exactly 1 is a man?

If 5 of the 10 are men it means that the other five are women. 
If in the technical support positions exactly 1 is a man it means that 4 are women.

The answer is:
C(5, 4)*C(5, 1) = 5*5=25 ways.

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The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.