Verified Solution • 2025–26 Session moderate

QJEEM19Ma70a1: JEE Main 2019 Mathematics - Class 11 JEEM19Ma70a1 Solution: A group of students comprises of 5 boys and n girls. If the…

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 :

Multiple Choice Options

  • A 24
  • B 25
  • C 27
  • D 28

Step-by-Step Verified Solution

Given that 5 Boy, n girls.

(1B, 2G) + (2B, 1G)

5C1.nC2+5C2.nC1=1750{}^5{C_1}.{}^n{C_2} + {}^5{C_2}.{}^n{C_1} = 1750

⇒5.n(n−1)2+10.n=1750\Rightarrow 5.{{n\left( {n - 1} \right)} \over 2} + 10.n = 1750

⇒n(n−1)2+2n=350\Rightarrow {{n\left( {n - 1} \right)} \over 2} + 2n = 350

⇒n2−n+4n=700\Rightarrow {n^2} - n + 4n = 700

⇒n2+3n−700=0\Rightarrow {n^2} + 3n - 700 = 0

⇒(n+28)(n−25)=0\Rightarrow (n + 28)(n - 25) = 0

⇒n=25,−28\Rightarrow n = 25, -28

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