Combinatorics

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Subsets of Boys and Girls

COMBIN-EZEQEJ

A club has $n$ boys and $n$ girls. Which two expressions equal the number of ways to select a subset of $n$ children from the club?

Select ALL that apply.

A

$\sum_{k=0}^n{n\choose k}^2$

B

$\sum_{k=0}^n{n\choose k}+\sum_{k=0}^n{n\choose n-k}$

C

$\sum_{k=0}^n{n\choose k}$

D

$2{n\choose n/2}{n\choose n/2}$

E

$2{n\choose 2}{n\choose 2}$

F

${2n\choose n}$