﻿ 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 : : Kaysons Education

# 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 :

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## Question

### Solution

Correct option is

2n – m – 1

1 ≤ n ≤ P

A = {1, 2, 3,…….,P}

And            = {m, m + 1,…….,n – 1,n}

No. of elements = n – m + 1

As  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 = 2n – m – 1

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