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}} $

Show Answer

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}}. $



sathee Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on

Please select your preferred language
कृपया अपनी पसंदीदा भाषा चुनें