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A publishing house plans to select 1 chief editor from 8 eligible candidates and 2 assistant editors from 12 eligible candidates. If no candidate is eligible for both roles, how many distinct sets of 3 hires are possible?

Explanation	Calculations	Help
$We first calculate the number of ways to choose one chief editor from eight eligible candidates.$	$\frac{8 !}{1 ! 7 !} = \frac{8 \times 7 !}{1 \times 7 !} = 8$	Theory & Tactics Method Card PC3-C Click to view full details
$We then calculate the number of ways to choose two assistant editors from twelve eligible candidates, where the two positions are identical.$	$\frac{12 !}{2 ! 10 !} = \frac{12 \times 11 \times 10 !}{2 \times 1 \times 10 !} = \frac{12 \times 11}{2 \times 1} = 66$	Theory & Tactics Method Card PC3-C Click to view full details
$Because the selections for chief editor and assistant editors are independent, we multiply these counts to find the total number of sets of three hires.$	$8 \times 66 = 528$	Theory & Tactics Method Card PC2-A Click to view full details

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D

A publishing house plans to select 1 chief editor from 8 eligible candidates and 2 assistant editors from 12 eligible candidates. If no candidate is eligible for both roles, how many distinct sets of 3 hires are possible?

Explanation	Calculations	Help
$We first calculate the number of ways to choose one chief editor from eight eligible candidates.$	$\frac{8 !}{1 ! 7 !} = \frac{8 \times 7 !}{1 \times 7 !} = 8$	Theory & Tactics Method Card PC3-C Click to view full details
$We then calculate the number of ways to choose two assistant editors from twelve eligible candidates, where the two positions are identical.$	$\frac{12 !}{2 ! 10 !} = \frac{12 \times 11 \times 10 !}{2 \times 1 \times 10 !} = \frac{12 \times 11}{2 \times 1} = 66$	Theory & Tactics Method Card PC3-C Click to view full details
$Because the selections for chief editor and assistant editors are independent, we multiply these counts to find the total number of sets of three hires.$	$8 \times 66 = 528$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

D