Question

If the total number of m-element subsets of the set \(A=\left\{a_{1}, a_{2}, \ldots . a_{n}\right\}\) is \(k\) times the number of \(m\) element subsets containing \(a_{4}\), then \(n\) is
(A) \((m-1) k\)
(B) \(m k\)
(C) \((m+1) k\)
(D) \((m+2) k\)

Answer 1

Ans: (B)
Hint : \(n_{c_{m}}=k \cdot{ }^{n-1} c_{m-1} \Rightarrow n=m k\)