Verified Solution • 2025–26 Session moderate

QJEEM22Mab5ad: JEE Main 2022 Mathematics - Class 11 JEEM22Mab5ad Solution: There are ten boys B 1 , B 2 , ......., B 10 and five girls G 1 …

There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is ___________.

Step-by-Step Verified Solution

Number of ways when B1 and B2 are not together

= Total number of ways of selecting 3 boys −- B1 and B2 are together

= 10C3 −- 8C1

= 10 . 9 . 81 . 2 . 3−8{{10\,.\,9\,.\,8} \over {1\,.\,2\,.\,3}} - 8

= 112

Number of ways to select 3 girls = 5C3 = 10

∴\therefore Total number of ways = 112 ×\times 10 = 1120

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