# Practice GMAT Problem Solving Question

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Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 10 candidates. She plans to have one working interview with 3 of the 10 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?

Correct Answer:

**B**- In this combinations problem, order is not important (i.e., Mariah having an interview with John Smith, Mary Jones and David Arlington is the same as an interview with Mary Jones, David Arlington and John Smith). Because order is not important, the solution involves the combination formula and not the permutation formula.
- The formula for a combination is:

_{n}C_{r}= n!/((n-r)!r!)

where n is the total number of selections available and r is the number of items to be selected. - For this problem the total number of selections, n, is 10 and the total number of items to be selected, r, is 3. So the combination formula is written and calculated as:

_{10}C_{3}= 10! /( (10 – 3)! * 3! )

= (10 * 9* 8) /( 3*2) = 720 / 6 = 120 - Since there are 120 combinations, it will take her 120 days to interview all possible combinations of job candidates in groups of three. So the correct answer is B.
- A common mistake is to use the permutation formula which would yield six times as many days or 720 days. Other common mistakes are to reverse the order for n and r in the combination formula.

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