JEE Main 2019MathematicsPermutation CombinationMediumMCQ

JEE Main 2019 — Permutation Combination Question with Solution

JEE Main 2019 (12 Apr Shift 2)

Question

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C25

Step-by-step explanation

(5) (n)
Boys Girls
2 1
1 2
Here total number of ways

=   5 C 2 ×   n C 1 + 5 C 1 ×   n C 2 =1750

⇒10n+5 n( n−1 ) 2 =1750

⇒ n 2 +3n−700=0

⇒n=−28, 25

n cannot be negative

Hence n=25

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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.