Question

Three people, A, B and C, enter a race. Write down the different orders in which they can finish first, second, and third.

Answer 1

a. The sample space for that will be {ABC,ACB,BAC,BCA,CAB,CBA}

where the first, second and third letter represents the respective places

Harry is correct as there are three possiblities for winner, two possibilities for second place and one possibility for third place.

b. People can finish a 4-person race in

`4*3*2`

The winner 4 ways , second place 3 ways and third place 2 ways.

People can finish a 6-person race in

`6*5*4`

The winner 6 ways , second place 5 ways and third place 4 ways.

People can finish a 10-person race in

`10*9*8`

The winner 10 ways , second place 9 ways and third place 8 ways.