1
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Question

# The total number of selections of at most n things from (2n+1) different things is 63. Then the value of n is

A
3
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B
2
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C
4
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D
none of these
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Solution

## The correct option is A 3The total number of selections of at most n things from (2n+1) different things i.e. selecting 1,2,3,......n things from (2n+1) things⟹ 2n+1C1+2n+1C2+2n+1C3+............................2n+1Cn⟹ 12(2n+1C1+2n+1C2+2n+1C3+............................2n+1C2n)⟹ 12(2n+1C0+2n+1C1+2n+1C2+2n+1C3+............................2n+1C2n+2n+1C2n+1)-1⟹12(22n+1)-1⟹22n−1=63⟹22n=26⇒n=3

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