Question

There are four cars entered into a pinewood derby race. In how many different orders can they cross the finish line, assuming there are no ties?

Answer 1

The number of different orders in which the cars can cross the finish line, assuming there are no ties = 24

For the first place , one of the four cars can win = 4C1

For the second place , one of the three cars left can come in second place = 3C1

For the third place ,one of the two cars left will come in third place = 2C1

For the fourth place only one car is left = 1

Total number of ways = 4C1 × 3C1 × 2C1 × 1

= 24