A group of students comprises of 5 boys and n | vedclass

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Question

Given $5$ boys and $n$ girls

Total ways of farming team of $3$ Members under given condition

 ${ = ^5}{C_1}{.^n}{C_2}{ + ^5}{C_2}{.^n}{C_1}

Vedclass · Accepted Answer

$25$

Vedclass · Answer

Given $5$ boys and $n$ girls

Total ways of farming team of $3$ Members under given condition

 ${ = ^5}{C_1}{.^n}{C_2}{ + ^5}{C_2}{.^n}{C_1}$

${ \Rightarrow ^5}{C_1}{.^n}{C_2}{ + ^5}{C_2}{.^n}{C_1} = 1750$

$ \Rightarrow \frac{{5n(n - 1)}}{2} + 10n = 1750$

$ \Rightarrow \frac{{n(n - 1)}}{2} + 2n = 350$

$ \Rightarrow {n^2} + 3n = 700$

$ \Rightarrow {n^2} + 3n - 700 = 0$

$ \Rightarrow n = 25$

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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