JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Permutations and Combinations

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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)24
(B)28
(C)27
(D)25✓ Correct

Answer: (D)

Solution

A team of

3

with at least one of each is either

1

boy and

2

girls or

2

boys and

1

girl, so

(1 5) (2 n) + (2 5) (1 n) = 1750

. That is

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

, which tidies to

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

, factoring as

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

. The positive root is

n = 25

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option

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