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 will one combination of five numbers will win? What is the probability of winning if 100 different lottery tickets are purchased?

Answer 1

Explanation:

Given

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.

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

here n=45, r=5

`^(45)C_5=(45!)/(40!5!)`

`^(45)C_5=1221759`

out of which there is only combination foe contest winning

`P=(1)/(1221759)`

When 100 different tickets are bought then

Probability of winning
`=(100)/(1221759)`