Question

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?

Answer 1

There are five ways of choosing one man. Having chosen 1 man there are 9C4 ways of choosing 4 from the remaining 9. Therefore the total number of ways is\[5\times \frac{9!}{5!4!}=5\times \frac{9\times 8\times 7\times 6}{4\times 3\times 2}=\]
Now you can finish it.