Question

The Lacrosse booster club is holding a raffle for a fundraiser. They will sell 100 tickets for $5 each and select 4 winners. All of the winners will win a giftcard to Chipotle. If every ticket is sold, in how many ways can the 4 winners be selected?

Answer 1

There are 3,921,225 ways to select the winners.

Explanation:

This problem is about combinations with no repetitions, because the same person can't win four times. It's a combinaction because the order of winning doesn't really matter.

Combinations without repetitions are defined as

`C_(n)^(r) =(n!)/(r!(n-r)!)`

Where
`n=100` and
`r=4`.

Replacing values, we have

`C_(100)^(4) =(100!)/(4!(100-4)!)=(100!)/(4! 96!)=(100 * 99 * 98 * 97 * 96!)/(4! * 96!)= (94,109,400)/(24)= 3,921,225`

Therefore, there are 3,921,225 ways to select the winners.

Additionally, as you can imagine, the probability of winning is extremely low, it would be 3,921,225 to 1.