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18 Apr 2022, 09:19
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E
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Difficulty:
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Question Stats:
70% (00:56) correct
30%
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wrong
based on 275
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A board of directors consists of 10 members. Three of those members are in leadership positions: President, Vice President, and Treasurer. If no individual can hold more than one leadership position, how many different ways are there to assign the three leadership positions?
(A) 6
(B) 24
(C) 120
(D) 540
(E) 720
(A) 6
(B) 24
(C) 120
(D) 540
(E) 720
18 Apr 2022, 10:13
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GMATNinja
total ways to select 3 members ; 10c3 ;
and ways in which 3 selected people can be chosen for positions ; 3*2*1 ; 6
10c3 * 6 ; 720
option E
PyjamaScientist
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18 Apr 2022, 20:43
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Counting method:
How many choices for the first place = \(10\). For second place = \(9\). For third place = \(8\). Total no. of possibilities = \(10 * 9 * 8 = 720.\)
Combinations method:
We need to choose \(3 \) people out of \(10\) people for the post of President, VP and Treasurer. Suppose we choose \(A, B,\) and \(C\) from \(10\) directors. But either one of them can take either position. So, we don't just need to choose \(3 \) people out of \(10\), we also need to jumble them among themselves as anyone can be President/VP/Treasurer among the three. Thus, it can be done in \(10_C_3\) * \(3!\) ways = \(720\).
How many choices for the first place = \(10\). For second place = \(9\). For third place = \(8\). Total no. of possibilities = \(10 * 9 * 8 = 720.\)
Combinations method:
We need to choose \(3 \) people out of \(10\) people for the post of President, VP and Treasurer. Suppose we choose \(A, B,\) and \(C\) from \(10\) directors. But either one of them can take either position. So, we don't just need to choose \(3 \) people out of \(10\), we also need to jumble them among themselves as anyone can be President/VP/Treasurer among the three. Thus, it can be done in \(10_C_3\) * \(3!\) ways = \(720\).
