Let 1 ≤ m

Question

Let 1 ≤ m < n ≤ 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) 2n-m-1=1 (B) 2n-m-1 (C) 2n-m (D)  2p-n+m-1

Tardigrade Admin · Accepted Answer

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 = 2n-m-1

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

$2^{n - m - 1} = 1$

$2^{n - m - 1}$

$2^{n - m}$

$2^{p - n + m - 1}$

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 = $2^{n - m - 1}$

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

2n−m−1=1

2n−m−1

2n−m

2p−n+m−1