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?

Question

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Respuesta :

nuuk nuuk · Answer 1 · 2019-12-23T11:42:51+01:00

Answer:

Step-by-step 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.

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

here n=45, r=5

[tex]^{45}C_5=\frac{45!}{40!5!}[/tex]

[tex]^{45}C_5=1221759[/tex]

out of which there is only combination foe contest winning

[tex]P=\frac{1}{1221759}[/tex]

When 100 different tickets are bought then

Probability of winning[tex]=\frac{100}{1221759}[/tex]