## Question

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 :

### Solution

2^{n – m – 1}

1 ≤ *m *< *n* ≤ *P*

* A = *{1, 2, 3,…….,*P*}

And *B *= {*m, m *+ 1,…….,*n* – 1,n}

No. of elements = *n – m *+ 1

As *m * and *n* will always be there in every subset, no. of elements in consideration are (*n – m *+ 1) – 2 =* n – m –* 1.

No. of subsets = 2^{n – m – 1}

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