Question

In a relay race, there are six teams $A,B,C,D,E$ and $F$. What is the probability that $A,B,C$ finish first, second, third respectively?

• A. $\frac{1}{2}$
• B. $\frac{1}{12}$
• C. $\frac{1}{60}$
• D. $\frac{1}{120}$

Answer 1

The correct option is D $\frac{1}{120}$

Now, the six teams can finish in $6!$ ways.

When A,B,C finish first, second, third then we only have to find out the number of ways in which the positions to the last three teams can be given. That can be done in $3!$ ways.

So, the required probability $=\frac{3!}{6!}=\frac{1}{120}$

Hence, D is correct.