JEE MAIN - Mathematics (2022 - 26th June Morning Shift - No. 14)
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 ___________.
Answer
1120
Explanation
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
= $${{10\,.\,9\,.\,8} \over {1\,.\,2\,.\,3}} - 8$$
= 112
Number of ways to select 3 girls = 5C3 = 10
$$\therefore$$ Total number of ways = 112 $$\times$$ 10 = 1120
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