JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Permutations and Combinations

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A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways the committee can be formed is:

(A)560
(B)1625✓ Correct
(C)1050
(D)575

Answer: (B)

Solution

The committee must have at least 2 Indians and double the number of foreigners as Indians. Let the number of Indians be

n

, then foreigners =

2 n

.

Possible cases:

$n = 2$ : Indians = 2, Foreigners = 4 → $(2 6) \times (4 8) = 15 \times 70 = 1050$
$n = 3$ : Indians = 3, Foreigners = 6 → $(3 6) \times (6 8) = 20 \times 28 = 560$
$n = 4$ : Indians = 4, Foreigners = 8 → $(4 6) \times (8 8) = 15 \times 1 = 15$

Total ways =

1050 + 560 + 15 = 1625

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Single correct option

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