2012-04-19 09:00:48

A company has ten applicants for four positions. If each applicant is qualified for each vacancy, how many possible ways can the company fill the four openings?

(A) 40
(B) 105
(C) 210
(D) 400
(E) 5040

The correct answer is C

Explanation: 4 positions to fill from 10 applicants means the question is looking for a combination: how many groups of four can be made from ten total? Therefore, the best approach to this is to use the combination formula: nCr = n!/(r!(n-r)!), where n is the number of objects available and r is the number taken at a time. Thus, here n = 10 and r = 4. Use these numbers in the formula to get:

10!                                     or            10!
4!(10-4)!                                          4!6!

This equals 210.