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A consulting firm will select 1 of 6 candidates for a managerial role and 2 of 14 candidates for two identical analyst positions. If no candidate is eligible for both roles, how many distinct sets of 3 hires are possible?

Explanation	Calculations	Help
$We first calculate the number of ways to choose one managerial candidate from six eligible candidates.$	$\frac{6 !}{1 ! 5 !} = \frac{6 \times 5 !}{1 \times 5 !} = 6$	Theory & Tactics Method Card PC3-C Click to view full details
$We then calculate the number of ways to choose two analysts from fourteen eligible candidates for identical positions.$	$\frac{14 !}{2 ! 12 !} = \frac{14 \times 13 \times 12 !}{2 \times 1 \times 12 !} = \frac{14 \times 13}{2 \times 1} = 91$	Theory & Tactics Method Card PC3-C Click to view full details
$Because the managerial selection and analyst selection are independent, we multiply these counts to find the total number of sets of three hires.$	$6 \times 91 = 546$	Theory & Tactics Method Card PC2-A Click to view full details

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B

A consulting firm will select 1 of 6 candidates for a managerial role and 2 of 14 candidates for two identical analyst positions. If no candidate is eligible for both roles, how many distinct sets of 3 hires are possible?

Explanation	Calculations	Help
$We first calculate the number of ways to choose one managerial candidate from six eligible candidates.$	$\frac{6 !}{1 ! 5 !} = \frac{6 \times 5 !}{1 \times 5 !} = 6$	Theory & Tactics Method Card PC3-C Click to view full details
$We then calculate the number of ways to choose two analysts from fourteen eligible candidates for identical positions.$	$\frac{14 !}{2 ! 12 !} = \frac{14 \times 13 \times 12 !}{2 \times 1 \times 12 !} = \frac{14 \times 13}{2 \times 1} = 91$	Theory & Tactics Method Card PC3-C Click to view full details
$Because the managerial selection and analyst selection are independent, we multiply these counts to find the total number of sets of three hires.$	$6 \times 91 = 546$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

B