Compute Probabilities Involving Permutations and Combinations
-To Play the Lottery $\$ 1$

Compute Probabilities Involving Permutations and Combinations
-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?

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) $\frac { 1 } { 5,864,443,200 } ; \frac { 1 } { 58,644,432 }$