Question

To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying a $1 for each five-number selection. What is the probability that a person with one combination of the five numbers will win?
What is the probability of winning if 100 different lottery tickets are purchased?

Answer 1

There are 45 numbers out of which 5 numbers are required to win an enormous sum of money

No of ways  in which 5 numbers can be selected out of 45 numbers.

$C_{45}^5=\frac{45!}{40!5!} =1221759$

out of which there is only combination foe contest winning

$P=\frac{1}{1221759}$

When 100 different tickets are bought then

Probability of winning: $\frac{100}{1221759}$

Probably of winning≈0,000082

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P.S. Hello from Russia :^)