Let S(k) denote the set of all one-to-one and onto functions from {1,2,3,...<k} to itself. Let p, q be two positive integers. Let S(p,q) be the set of all T in S(p+q) such that T(1)<T(2)<...<T(p) and T(p+1)<T(p+2)<...<T(p+q). The number of elements in S(13,29) is?
MY approach is for S(13,29) T(1)<T(2)<...<T(13) and T(14)<T(15)<...<T(42) for first 13 elements we can selects any 13 elements from 42 and map them in ascending order and remaining 29 elements will be mapped in ascending order automatically. So, the answer should be C(42,13). I wish to confirm if I haven't overlooked something
