Question number 8?

8.
To form a subset B, choose 11 elements from the 22 elements of A.
Number of possible subset B = ²²C₁₁

Total number of elements in all possible subsets B = 11 × ²²C₁₁

Consider elements in all possible subsets B.
Number of "1" = Number of "2" = Number of "3" = …… = Number of "22" = 11 × ²²C₁₁ / 22

Sum of elements in all possible subsets B
= {11 × ²²C₁₁ / 22} × (1 + 2 + 3 + …… + 22)
= {11 × [22! / (11! 11!)] / 22} × [22 × (1 + 22) / 2]
= {11 × [22 × 21! / (11 × 10! 11!)] / 22} × [22 × 23 / 2]
= [21! / (10! × 11!)] × 253
= ²¹C₁₀ × 253
= 253 ²¹C₁₀

The answer: d) 253 ²¹C₁₀