JEE Main 2019MathematicsPermutation CombinationEasyMCQ

JEE Main 2019 — Permutation Combination Question with Solution

JEE Main 2019 (09 Apr Shift 1)

Question

A committee of 11 member is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:

Choose an option

Show full solutionCorrect option: C
Correct answer
Cm=n=78

Step-by-step explanation

m=(6M, 5F)+(7M, 4F)+(8M, 3F)

=C6 8×C5 5+C7 8×C4 5+C8 8×C3 5

=28×1+8×5+1×10=78

n=(3F, 8M)+(4F, 7M)+(5F, 6M)

=C3 5×C8 8+C4 5×C7 8+C5 5×C6 8

=10×1+5×8+1×28=78

Hence, m=n=78.

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About this question

This is a previous-year question from JEE Main 2019, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.