To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying $1 for eachfive-number selection. If the five numbers picked are the same as the ones drawn by the lottery, an enormoussum of money is bestowed. What is the probability that a person with one combination of five numbers willwin? What is the probability of winning if 100 different lottery tickets are purchased?
A) $\frac { 1 } { 1,221,759 } ; \frac { 100 } { 1,221,759 }$
B) $\frac { 1 } { 146,611,080 } ; \frac { 10 } { 14,661,108 }$
C) $\frac { 1 } { 8,145,060 } ; \frac { 1 } { 814,506 }$
D) $\frac { 1 } { 5,864,443,200 } ; \frac { 1 } { 58,644,432 }$

Question

To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying $1 for eachfive-number selection. If the five numbers picked are the same as the ones drawn by the lottery, an enormoussum of money is bestowed. What is the probability that a person with one combination of five numbers willwin? What is the probability of winning if 100 different lottery tickets are purchased? 
A) $\frac { 1 } { 1,221,759 } ; \frac { 100 } { 1,221,759 }$
B) $\frac { 1 } { 146,611,080 } ; \frac { 10 } { 14,661,108 }$
C) $\frac { 1 } { 8,145,060 } ; \frac { 1 } { 814,506 }$
D) $\frac { 1 } { 5,864,443,200 } ; \frac { 1 } { 58,644,432 }$

Quizplus · Accepted Answer

The probability of winning with one combination is calculated by finding the number of ways to choose 5 numbers out of 45, which is $\binom{45}{5} = 1,221,759$, so the probability is $\frac{1}{1,221,759}$. If 100 different lottery tickets are purchased, the probability of winning increases linearly, making it $\frac{100}{1,221,759}$.

To Play the Lottery in a Certain State, a Person 11,221,759;1001,221,759\frac { 1 } { 1,221,759 } ; \frac { 100 } { 1,221,759 }1,221,7591​;1,221,759100​

To Play the Lottery in a Certain State, a Person $\frac { 1 } { 1,221,759 } ; \frac { 100 } { 1,221,759 }$