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

A committee of 11 members is to be formed from 8 males and 5 females. If

m

is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:

(A) $n = m - 8$
(B) $m + n = 68$
(C) $m = n = 78$ ✓ Correct
(D) $m = n = 68$

Answer: (C)

Solution

From

13

people,

8

men and

5

women, we pick

11

, leaving only

2

out. Since at most

2

can be left out, at least

6

of the

8

men are always in and at least

3

of the

5

women are always in automatically. So both counts are just the number of ways to choose any

11

from

13

m = n = (11 13) = (2 13) = 78

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

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