Mathematics

Problem

Let set

A = \{1, 2, 3, \dots, 22\}

. Set

B

is a subset of

A

and

B

has exactly 11 elements, find the sum of elements of all possible subsets

B

. (a)

252 \cdot {}^{21}C_{11}

(b)

230 \cdot {}^{21}C_{10}

(c)

253 \cdot {}^{21}C_9

(d)

253 \cdot {}^{21}C_{10}