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

1 answer
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

Answers

Answer:Option AStep-by-step 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[tex]^{12}C_3[/tex][tex]220[/tex]Number of groups that can be formed when judges pick three contestants[tex]^{12}C_4\\495[/tex]Number of more  groups that can be formed if the judges  pick four instead of three[tex]= 495-220 = 275[/tex]Hence, option A is correct

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