26) In a relay race there are five teams A, B, C, D, E i) What is the probability - Maths - Probability

Question

26) In a relay race there are five teams A, B, C, D, E
i) What is the probability that A, B, C finish first, second and
third respectively
ii) What is the probability that A, B, C are first three to finish
(in any order)
iii) What is the probability that A and E finish first and last
respectively

Tejaswi · Accepted Answer

Dear Student,

(i)Total number of ways A , B , C , D and E can finish the race = 5!If A, B, C  finish 1st 2nd and 3rd respectively, then D &E can finish in 2 ways
So, probability= 25!=160(ii)Number of arrangements when A,B,C  finish in top 3 = 3!Number of ways D &E can finish in bottom 2 = 2!Total number of required ways = 3!
2!So, probability= 3!
2!5!=110(iii)If A&E finish first and last place respectively , number of ways B,C &D can take remaining positions =3!So, probability= 3!5!=120

Regards,