In how many ways can two distinct subsets of the set `A` of `k(kgeq2)` elements be selected so that they haves exactly two common elements?

In how many ways can we select two vertices in a hexagon?

In how many ways can two squares be chosen on a 8 xx 8 chessboard such that they have only one corner in common?

The number of one element subset,the number of two element subsets and the number of three element subsets o fa set containing more than three elements are consecutive terms of an A.P.The number of elements in the set can be

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :

A set A has n elements.A subset P of A is selected at random.Returning the elements of P ,the set A is formed again and then a subset Q is selected from it.Find the probability that P and Q have no common element.

In how many ways can 576 be expressed as the product of two distinct factors?

P is a set containing n elements . A subset A of P is chosen and the set P is reconstructed by replacing the element of A. B such that A and B have no common elements, is