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 $=7 ! \times{ }^8 P_3=7 ! \times 8 \times 7 \times 6$
$=7 ! \times 336$