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At a technology firm, the hiring committee will select 1 of 6 candidates to fill a project manager position and 2 of 9 different candidates to fill two identical software developer positions. If no candidate is eligible for both roles, how many different sets of 3 hires are possible?

Explanation	Calculations	Help
$We first calculate the number of ways to choose one project manager from six eligible candidates.$	$\frac{6 !}{1 ! 5 !} = \frac{6 \times 5 !}{1 \times 5 !} = 6$	Theory & Tactics Method Card PC3-C Click to view full details
$We then calculate the number of ways to choose two software developers from nine eligible candidates, where the two positions are identical.$	$\frac{9 !}{2 ! 7 !} = \frac{9 \times 8 \times 7 !}{2 \times 1 \times 7 !} = \frac{9 \times 8}{2 \times 1} = 36$	Theory & Tactics Method Card PC3-C Click to view full details
$Because the project manager selection and the software developer selection are independent, we multiply these counts to find the total number of sets of three hires.$	$6 \times 36 = 216$	Theory & Tactics Method Card PC2-A Click to view full details

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B

At a technology firm, the hiring committee will select 1 of 6 candidates to fill a project manager position and 2 of 9 different candidates to fill two identical software developer positions. If no candidate is eligible for both roles, how many different sets of 3 hires are possible?

Explanation	Calculations	Help
$We first calculate the number of ways to choose one project manager from six eligible candidates.$	$\frac{6 !}{1 ! 5 !} = \frac{6 \times 5 !}{1 \times 5 !} = 6$	Theory & Tactics Method Card PC3-C Click to view full details
$We then calculate the number of ways to choose two software developers from nine eligible candidates, where the two positions are identical.$	$\frac{9 !}{2 ! 7 !} = \frac{9 \times 8 \times 7 !}{2 \times 1 \times 7 !} = \frac{9 \times 8}{2 \times 1} = 36$	Theory & Tactics Method Card PC3-C Click to view full details
$Because the project manager selection and the software developer selection are independent, we multiply these counts to find the total number of sets of three hires.$	$6 \times 36 = 216$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

B