Question

Of the $12$ members of a high school drama club, $8$ are seniors. The club plans to establish and $8-$member committee to interview potential club members. If exactly $6$ members of the committee must be seniors, calculate the total number of possible committees.

• A. $21$
• B. $34$
• C. $168$
• D. $336$
• E. $495$

Answer 1

Answer: (C)

$168$

In $12$ members club, $8$ members are seniors and $4$ members are non seniors.
Given that in a selected committee, there should be exactly $6$ seniors.
So, total number of possible committees is ${{}^{8}C}_6\times {{}^{4}C}_2=28\times 6=168$.