If the total number of m-element subsets of the set A = {a₁, a₂, ..., a_n} is k times the number of m element subsets containing a₄, then n is

A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she make up his/her choice of 6 questions?

There are 7 greeting cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,

The number of selection of n objects from 2n objects of which n are identical and the rest are different, is