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Q.

Let $A = {1, 2, 3, - - - - 22},$ $B$ is a subset of $A$ having exactly 11 elements. The sum of elements of all possible subsets of $B$ is

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a

$253 \times^{21} C_{10}$

b

$230 \times^{21} C_{11}$

c

$253 \times^{21} C_{9}$

d

$252 \times^{21} C_{11}$

answer is A.

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Detailed Solution

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$2700 (1 + 2 + 3 + 4 + ...... + 9) + 810 (1 + 4 + 9) + 27 (1 + 2 + 3 + ..... + 9)$

$= 2700 \times 45 + 810 \times 14 + 27 \times 45 = 134055$

(or)

$22_{C_{11}} \frac{[1 + 2 + 3 + - - - + 22]}{2}$

$= \frac{253}{2} {.22}_{C_{11}}$

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