Question

Let $1 \leq m < n \leq p$. The number of subsets of the set $A =\{1,2,3, \ldots \ldots \ldots p \}$ having $m , n$ as the least and the greatest elements respectively, is

• A. $2^{n-m-1}=1$
• B. $2^{n-m-1}$
• C. $2^{n-m}$
• D. $\quad 2^{p-n+m-1}$

Answer 1

Answer: (B)

Between $m$ and $n$, there are $n - m -1$ elements. Each subset contains $m$ and $n$ and for all of other $n - m -1$ elements, there are two possibilities so, no. of subset = $2^{n-m-1}$