In a relay race there are five teams A, B, C, | vedclass

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Question

(A) The total number of ways in which the first three positions can be filled by $5$ teams is given by the permutation formula $^{5}P_{3}$.$^{5}P_{3}

Vedclass · Accepted Answer

$\frac{1}{60}$

Vedclass · Answer

(A) The total number of ways in which the first three positions can be filled by $5$ teams is given by the permutation formula $^{5}P_{3}$.$^{5}P_{3} = \frac{5!}{(5-3)!} = 5 	imes 4 	imes 3 = 60$.Since each finishing order is equally likely,the probability of any specific order is $\frac{1}{60}$.The event where $A, B$ and $C$ finish first,second and third respectively corresponds to exactly one specific outcome: $(A, B, C)$.Therefore,the probability is $\frac{1}{60}$.

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

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