SOLUTION: A firm has 5 different positions to fill and 15 applicants from which to choose. All applicants are equally qualified for all 5 positions. In how many ways can the firm fill the po

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Question 1029763: A firm has 5 different positions to fill and 15 applicants from which to choose. All applicants are equally qualified for all 5 positions. In how many ways can the firm fill the positions? show working please.
Answer by ikleyn(52780) About Me  (Show Source):
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A firm has 5 different positions to fill and 15 applicants from which to choose. All applicants are equally qualified for all 5 positions. In how many ways can the firm fill the positions? show working please.
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In how many ways one can choose 5 objects from the set of 15?

By C%5B15%5D%5E5 = %2815%2A14%2A13%2A12%2A11%29%2F%281%2A2%2A3%2A4%2A5%29 = 3*7*13*11 = 3003 ways.

C%5B15%5D%5E5 is the number of combinations of 15 things taken 5 at a time.

On combinations see the lesson Introduction to Combinations in this site.