Probability question

How many ways are there to pick a first place, second place, and third place winner in a contest with 40 participants?

There are 40 ways to pick the first place winner (all 40 contestants). Then, after you picked the first place winner, there are 39 ways you pick the second place winner (all 40 contestants except who you picked for first place). Next, after you picked the second place winner, there are 38 ways you pick the third place winner (all 40 contestants except who are first and second). Therefore, there are 40*39*38 = 59,280 ways to pick winners.

I hope this helps!

First place = 40C1.

After filling up the 1st, the second place in 39C1 ways.

After filling up the second place, the third by 38C1 ways.

40C1 x 39C1 x 38C1.
using a calculator, the answer is 59280.

As nCn = n, you could simply write 40 x 39 x 38 = 59280, but knowing how to use the choose function can help in similar problems.