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JEE Main 2019 · 12 Apr · Shift II

JEE Main 2019 Mathematics question on Permutations and Combinations

A group of students comprises of 5 boys and nn 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 nn is equal to
  1. A.
    28
  2. B.
    27
  3. C.
    25
  4. D.
    24
Show answer and solution

Correct option: C

Solution

The number of teams with at least one boy and at least one girl = (2 boys, 1 girl) + (1 boy, 2 girls) = C(5,2)·C(n,1) + C(5,1)·C(n,2) = 10n + 5·n(n-1)/2.

Setting equal to 1750: 10n + 5n(n-1)/2 = 1750 → multiply by 2: 20n + 5n(n-1) = 3500 → 5n(n+3) = 3500 → n(n+3) = 700.

Trying n = 25: 25 × 28 = 700 ✓. So n = 25.

[JEE Main 2019 · 12 Apr · Shift II]

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