Question

In a class of 10 students there are 3 girls $A,B,C$. The number of different ways they can be arranged in a row such that no two of three girls are consecutive are

• A. $4!\times 300$
• B. $7!\times 336$
• C. $6!\times 300$
• D. $6!\times 336$

Answer 1

Answer: (B)

$\times B_1\times B_2\times B_3\times B_4\times B_5\times B_6\times B_7\times$
First, we arrange 7 boys in 7 ! ways.
Now for girls, we have eight places and 3 girls need to be arranged.
This can be done in ${}^8{P}_3$ ways.
Total ways $=7!\times {}^8{P}_3=7!\times 8\times 7\times 6$
$=7!\times 336$