Find the number of ordered pairs `(S,T)` of subsets of the set `A={1,2,3,4,5,6}` such that `S uu T` contains exactly three elements

The number of unordered pair (A,B), of subsets of the set S={1,2,3,4,5,6,7,8,9,10} Such that A nn B=O/ and A uu B=S, is

The number of proper subsets of the set : A= {1,2,3,4,5} is :

Find the number of subsets X of {1,2,3,4,5,6,7,8,9,10} such that x contains at least two elements and that no two elements of X differ by 1.

Find the number of subsets that can be formed from the set A={4,5,6}

The total number of subset of the set {1,2,…,10} which do not contain the element 6 is

Find the number of all three elements subsets of the set {a_(1),a_(2),a_(3),.............a_(n)} which contain a_(3) .

Find the unit digit of the number of non empty subsets S of {1,2,3,4,5,6,7,8,9,10,11,12} such that no two consecutive integers belong to S and if S contains k elements it contains no elements less than k

If A=[1,2,3,4,5,6] then how many subsets of A contain the element 2, 3 and 5?

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset of A is again chosen. Find the number of ways of choosing P and Q, so that (i) P capQ contains exactly r elements. (ii) PcapQ contains exactly 2 elements. (iii) P cap Q=phi