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A set consists of (2n+1) elements. If the number of subsets of this set which consist of at most n elements is 8192. Find out the value of n.
Ans: The following set has (2n + 1) elements. The number of subsets of this set comprising at the most n elements is following by formula
2n + 1C0 + 2n + 1C1 + 2n + 1C2 + ..... 2n + 1Cn = (1/2)22n+1 =2 2n
This figure is given to be 8192, so 22n = 8192 ⇔ 22n = 213 ⇔ 2n = 13 ⇔ n = 6.5
Hence n = 6.5.
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