Question

6 boys and 3 girls are randomly placed in a row. Determine the probability of no two girls being placed adjacently.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The number of ways that no two girls are placed together is the number of ways in which 3 places marked with G are selected out of the SEVEN places.

___B___B___B___B____B____B____

This can be done in ${}^7$C${}_3$ ways.

Total no. of ways in which balls can be arranged = $\frac{10!}{(7!\times 3!)}$ = ${}^{10}$C${}_3$. So, required probability = $\frac{{}^7{C}_3}{{}^{10}{C}_3}$ = $\frac{7}{24}$.

Hence option(b)