Question

question 16 (5 points)
choose the one alternative that best completes the statement or answers the
question.
to play the lottery in a certain state, a person has to correctly select 5 out of 45
numbers, paying $1 for each five - number selection. if the five numbers picked are
the same as the ones drawn by the lottery, an enormous sum of money is bestowed.
what is the probability that a person with one combination of five numbers will win?
what is the probability of winning if 100 different lottery tickets are purchased?

Explanation:

Step1: Calculate the number of combinations for 1 ticket

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 45\) and \(r=5\).

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The probability of winning with 1 ticket is \(\frac{1}{1221759}\)

Step2: Calculate the probability for 100 tickets

If there are 100 different tickets, the probability of winning is \(\frac{100}{1221759}\)

Answer:

\(\frac{1}{1,221,759};\frac{100}{1,221,759}\)