Statement I: A and B select objects from two different groups, each containing 20 distinct objects. The number of choices with B selecting strictly more objects than A (including A selecting none) is

Question

Statement I: A and B select objects from two different groups, each containing 20 distinct objects. The number of choices with B selecting strictly more objects than A (including A selecting none) is $(2^{40} - (20 40)) /2$ . Statement II: $\sum_{0 \leq i < j \leq n} (i n) (j n) = (2^{2 n} - (n 2 n)) /2$ .

Options:

Answer:

A

Solution:

Count each pair of subset sizes $i < j$ by $(i 20) (j 20)$ and use the identity in II with $n = 20$ . The printed source says B, though II directly explains I.

TestHub · Accepted Answer

Count each pair of subset sizes i < j by ( i 20 ​ ) ( j 20 ​ ) and use the identity in II with n = 20 . The printed source says B, though II directly explains I.

Mathematics - Permutation & Combination Question with Solution | TestHub

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