# 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 : Option 1) 28 Option 2) 27 Option 3) 25 Option 4) 24

atleast one boy & one girl :

( 1B & 2G) + ( 2B & 1G)

$_{1}^{5}C\textrm{}._{2}^{n}C\textrm{}+_{2}^{5}C\textrm{}._{1}^{n}C\textrm{}=1750$

$=> 5 \frac{n(n-1)}{2}+10.n=1750$

$=> \frac{n(n-1)}{2}+2.n=350$

$=> n^{2}-n+4n=700$

$=> n^{2}+3n-700=0$

$=> (n+28)(n-25)=0$

$=> n=25,-28$

As, n cannot be -ve so, n = 25

Option 1)

28

Option 2)

27

Option 3)

25

Option 4)

24

### Preparation Products

##### Knockout JEE Main July 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
##### Rank Booster JEE Main 2020

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 9999/- ₹ 4999/-
##### Test Series JEE Main July 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 1999/-
##### Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 17999/- ₹ 11999/-