Question

If $8$ boys are arranged in a row what is the probability that $3$ particular boys always sit together?

• A. $\frac{3}{28}$
• B. $\frac{5}{28}$
• C. $\frac{3}{16}$
• D. $\frac{5}{16}$

Answer 1

The correct option is A $\frac{3}{28}$

Total number of boys to be arranged in a row is $8$.

Therefore, the number of ways of arranging them is $8!$ ways.

Given that three particular boys should always sit together.

Hence, just group these three boys together and consider as a single person.
Therefore, we can take total number of boys as $6$. These $6$ boys can be arranged in $6!$ ways.
We had grouped three boys together. These three boys can be arranged among themselves in $3!$ ways.
Hence, required number of ways to arrange boys is $6!\times 3!$.

Therefore, the required probability $\frac{6!\times 3!}{8!}=\frac{3}{28}$

Hence, the probability that $3$ particular boys always sit together is $\frac{3}{28}$.