A partition of a set A is a collection of disjoint subsets of A whose union is A.
Let A be a set of n elements. If T(n,k) denotes number of partitions of A such that size of each partition is k(1<=k<=n), then which of the following is true?
(A) T(n,k) = T(n-1,k-1)+k*T(n-1,k) if n!=k and k>1 =1 else
(B) T(n,k) = T(n-1,k-1)+k*T(n-1,k) if n!=k and k>+1 =1 else
(C) T(n,k) = 2*T(n-1,k-1) if n!=k and k>=1 =1 else
(D) T(n,k) = k*T(n-1,k-1) if n!=k and k>1=1 =1 else