Question

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 1

The correct answer is 1120
Required number of ways = Total ways of selection – ways in which B1 and B2 are present together.
$=^{10}C_3⋅^5C_3−^8C_1⋅^5C_3$
=10(120−8)
= 1120