In how any different ways can a set `A` of `3n` elements be partitioned into 3 subsets of equal number of elements? The subsets `P ,Q ,R` form a partition if `PuuQuuR=A ,PnnR=varphi,QnnR=varphi,RnnP=varphidot`

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?

Two finite sets A and B have respectively p and q elements. If the total number of subsets of A is 56 more than the total number of subsets of B, then find the values of p and q.

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of AxxB having 3 or more elements is____

The set S:={1,2,3…..12} is to be partitioned into three sets A,B,C of equal size thus AcupBcupC=S,AcapB=BcapC=AcapC=phi the number of ways to partition S is

If the set of natural numbers is partitioned into subsets S_1={1},S_2={2,3},S_3={4,5,6} and so on then find the sum of the terms in S_(50)dot

Find the number of all three elements subsets of the set {a_1, a_2, a_3, ........... a_n} which contain a_3dot

Let A be a set of n(ge 3) distinct elements. The number of triplets (x, y, z) of the elements of A in which ar least two coordinates are equal is

The set S={1,2,3,...,12} is to be partitioned into three sets A,B,C of equal size. Thus AcupBcupC=S, AcapB=B capC=C capA=phi. Find the number of ways to partition S.

Set A has m distinct elements and set B has n distinct elements. Then how many different mappings from set A to set B can be formed?

A is a set containing n different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P . A subset Q of A is again chosen. The number of ways of choosing P and Q so that PnnQ contains exactly two elements is a. .^n C_3xx2^n b. .^n C_2xx3^(n-2) c. 3^(n-1) d. none of these