Permutations And Combinations Question 344

Question: Let $ 1\le m<n\le 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

Options:

A) $ {2^{n-m-1}}-1 $

B) $ {2^{n-m-1}} $

C) $ {2^{n-m}} $

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

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Answer:

Correct Answer: B

Solution:

  • [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 element, there are two possibilities so, no. of subset $ ={2^{n-m-1}}. $