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Question

A set contains (2n+1) elements. The number of sub-sets of the set which

contain at most n elements is



Your Answer
A

Your Answer
B

Your Answer
C

Correct Answer
D


Solution

The correct option is D


The number of sub-sets of the set which contain at most n elements is

2n+1C0+2n+1C1+.........+2n+1Cn = S (Say)

Then 2S = 2(2n+1C0+2n+1C1+.........+2n+1Cn)

= (2n+1C0+2n+1C2n+1)+(2n+1C1+2n+1C2n)+......+(2n+1Cn+2n+1Cn+1)     {nCr=nCnr}

= 2n+1C0+2n+1C1+..........+2n+1C2n+1 =22n+1

S = 22n

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