GMAT Quantitative Reasoning Practice Test 2

Question : 19 of 100

Marks: +1, -0

What is the number of different ways to choose a chairman, two deputies and two assistants for the class committee out of 7 students up for election?

Solution:

There are 7 different choices for chairman,

\;6 C_2=\;{6 !}/{2 ! × 4 !}=\;{6 × 5}/{2 × 1}=15

\;4 C_2=\;{4 !}/{2 ! × 2 !}=\;{4 × 3}/{2 × 1}=6

choices for the two deputies (choosing 2 out of 6 ), and choices for the two assistants.
The total is

7 × 15 × 6=630

choices.

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