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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2019Permutations and Combinations

Solution:

$^{5}C_{1} . ^{n}C_{2} + ^{5}C_{2} . ^{n}C_{1} \, = 1750$
$n^2 + 3n = 700$
$\therefore \, \, n = 25$