Question

There are ten boys $B_1,B_2,\dots ,B_{10}$ and five girls $G_1$, $G_2,\dots ,G_5$ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both $B_1$ and $B_2$ together should not be the members of a group, is________

Answer 1

Answer: 1120

$n(B)=10$
$n(a)=5$
The number of ways of forming a group of $3$ girls of $3$ boys.
$={}^{10}{C}_3\times {}^5{C}_3$
$=\frac{10\times 9\times 8}{3\times 2}\times \frac{5\times 4}{2}=1200$
The number of ways when two particular boys $B_1$ of $B_2$ be the member of group together
$={}^8{C}_1\times {}^5{C}_3=8\times 10=80$
Number of ways when boys $B_1$ of $B_2$ hot in the same group together
$=1200\times 80=1120$