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.

Answer 1

Dear Student,

$$\begin{gathered} \left(i\right) \\ TotalnumberofwaysA,B,C,DandEcanfinishtherace=5! \\ IfA,B,Cfinish1st2ndand3rdrespectively,thenD\&Ecanfinishin2ways. \\ So,probability=\frac{2}{5!}=\frac{1}{60} \\ \left(ii\right) \\ NumberofarrangementswhenA,B,Cfinishintop3=3! \\ NumberofwaysD\&Ecanfinishinbottom2=2! \\ Totalnumberofrequiredways=3!.2! \\ So,probability=\frac{3!.2!}{5!}=\frac{1}{10} \\ \left(iii\right) \\ IfA\&Efinishfirstandlastplacerespectively,numberofwaysB,C\&Dcantakeremainingpositions=3! \\ So,probability=\frac{3!}{5!}=\frac{1}{20} \end{gathered}$$

Regards,