Question

11. Twelve contestants are competing to be 15.

on American Idol. The judges will keep either way
three or four of the contestants. How many
more groups would be formed if the judges
pick four instead of three?
A) 275
B) 715
C) 792
D) 10,560

Answer 1

Option A

Explanation:

Out of 12 contestants, the judges will select either 3 or 4 contestant.

Number of groups that can be formed when judges pick three contestants

`^(12)C_3`

`220`

Number of groups that can be formed when judges pick three contestants

`^(12)C_4\\495`

Number of more groups that can be formed if the judges pick four instead of three

`= 495-220 = 275`

Hence, option A is correct