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kogti [31]
3 years ago
12

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?
Mathematics
1 answer:
Nadusha1986 [10]3 years ago
3 0

Answer:

<h2>There are 3,921,225 ways to select the winners.</h2>

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

C_{n}^{r}  =\frac{n!}{r!(n-r)!}

Where n=100 and r=4.

Replacing values, we have

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

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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