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JEE Main 2019 · 9 Jan · Shift I

JEE Main 2019 Mathematics question on Permutations and Combinations

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys AA and BB, who refuse to be the members of the same team, is
  1. A.
    350
  2. B.
    500
  3. C.
    200
  4. D.
    300
Show answer and solution

Correct option: D

Solution

Total teams without restriction: C(5,2) × C(7,3) = 10 × 35 = 350.

Teams where both A and B are included: fix A and B, choose 1 more boy from remaining 5, and 2 girls from 5: C(5,1) × C(5,2) = 5 × 10 = 50.

Valid teams = 350 - 50 = 300.

[JEE Main 2019 · 9 Jan · Shift I]

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