A is a set containing n elemments. A subset `P_(1)` of A is chosen. The set A is reconstructed by replacing the elements of `P_(1)`. Next, a subset `P_(1)` to `A` is chosen and againn the set is reconstructed by replacing the elements of `P_(2)`. In this way `m(gt1)` subsets `P_(1),P_(2), . ..,P_(m)` of A are chosen. find the number of ways of choosing `P_(1),P_(2), . . .,P_(m)`, so that
`P_(1)capP_(2)capP_(3)cap . .. cap P_(m)=phi`

Answer

(i) `(m+1)^(n)`
(ii) `(2^(m)-1)^(n)`