Question

In Example 28 , the number of ways of choosing A and B such that A = B, is
A. `2^(n)`
B. `3^(n)`
C. `""^(2n)C_(n)`
D. none of these

Answer 1

Correct Answer - a
Suppose A contains r `(0 le r le n)` elements. Then B
also contain r elements . In this case the number of ways of
choosing A and B is `""^(n)C_(r)xx""^(n)C_(r) = (""^(n)C_(r))^(2)` . But r, can very from 0 to
n. so, the number of ways of choosing A and B is
`sum_(r=0)^(n) (""^(n)C_(r))^(2) sum_(r=0)^(n)C_(r)""^(2) = C_(0)""^(2) + C_(1)""^(2) +...+ C_(n)""^(2)= ""^(2n)C_(n)`