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Combinatorics

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Moderate

More Girls Than Boys

COMBIN-VNWLQX

A club has $n$ boys and $n+1$ girls for some $n\geq 3$.

How many ways are there to select 3 children from the club if more girls than boys must be selected?

A

${2n+1\choose 3} + {2n+1\choose 2}$

B

${n+1\choose 3} +{n\choose 2}$

C

${2n+1\choose 3}$

D

${n\choose 3} +{n\choose 2}$

E

${n+1\choose 3}{n\choose 0} + {n\choose 2}{n\choose 1}$