Question

Five people, A, B, C, D, and E are equally qualified runners. They run a one - km sprint,
and the order of finish is recorded.

Number of orders of finish is?

Probability that runners come in order E, D C, B, A is ?

Probability that runners come in order E, D C, B, A is ?

Answer 1

Question (a)

Since there are 5 people running,

Number of people who can finish in 1^st place = 5 (any one of them)

Number of people who can finish in 2^nd place = 4 (since one of them has already finished 1^st)

Number of people who can finish in 3^rd place = 3 (since two of them has already finished 1^st and 2^nd)

Number of people who can finish in 4^th place = 2 (since theee of them has already finished 1^st , 2^nd and 3^rd​​​​​​​)

Number of people who can finish in 5^th place = 1 (since remaining runners have finished in first 4 places)

So Number of orders of finish = 5 * 4 * 3 * 2 *1

= 120

Question (b)

Probability that runners come in order E, D C, B, A is ?

Number of ways in which the five runners can finish in the order E, D C, B, A is 1

Number of ways in which the five runners can finsih the race = 120 ways

Probability that runners come in order E, D C, B, A = 1/120

= 0.008333

Question (c) is same as Question (b)

Even if the order is different that that of the question (b), the probability will remain same which is 0.008333 since if the order in which the five runners finish is given, the number of ways they can finish the race is only that order