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 :

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 : (A) 25 (B) 28 (C) 27 (D) 24

Tardigrade Admin · Accepted Answer

5C1 . nC2 + 5C2 . nC1 = 1750 n2 + 3n = 700 ∴ n = 25

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 :

25

28

27

24

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

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 :

25

28

27

24

5C1​.nC2​+5C2​.nC1​=1750 n2+3n=700 ∴n=25

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 :

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