In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)
In a relay race there are five teams $A, \,B, \,C, \,D$ and $E$. What is the probability that $A,\, B$ and $C$ are first three to finish (in any order) (Assume that all finishing orders are equally likely)
If we consider the sample space consisting of all finishing orders in the first three places, we will have $^{5} P _{3},$ i.e., $, \frac{5 \,!}{(5-3) \,!}$ $=5 \times 4 \times 3=60$ sample points, each with a probability of $\frac{1}{60}$.
$A$, $B$ and $C$ are the first three finishers.
There will be $3 \,!$ arrangements for $A, \,B$ and $C$.
Therefore, the sample points corresponding to this event will be $3 \,!$ in number.
So $P( A , \,B $ and $C$ are first three to finish) $=\frac{3\, !}{60}=\frac{6}{60}=\frac{1}{10}$
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