JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Permutations and Combinations

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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 A and B, who refuse to be the members of the same team, is:

(A)500
(B)200
(C)300✓ Correct
(D)350

Answer: (C)

Solution

Count all valid teams, then strike out the forbidden ones. Choosing

2

girls from

5

and

3

boys from

7

gives

(2 5) (3 7) = 10 \times 35 = 350

teams. The teams putting both A and B together use those two boys plus one of the remaining five and any two girls:

(2 5) (1 5) = 10 \times 5 = 50

. Subtracting,

350 - 50 = 300

teams keep A and B apart.

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

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