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 :

Answer:

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

Step-by-step 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

[tex]C_{n}^{r} =\frac{n!}{r!(n-r)!}[/tex]

Where [tex]n=100[/tex] and [tex]r=4[/tex].

Replacing values, we have

[tex]C_{100}^{4} =\frac{100!}{4!(100-4)!}=\frac{100!}{4! 96!}=\frac{100 \times 99 \times 98 \times 97 \times 96!}{4! \times 96!}= \frac{94,109,400}{24}= 3,921,225[/tex]

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.

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