How do I solve this?

Question

To play a certain lottery, a person has to correctly select 5 out of 60 numbers, paying $1 for each five-number selection. What is the probability of winning if 100 different lottery tickets are purchased?

Answer 1

Take one lottery ticket. The chances of correctly selecting a winning number as the first number are 1/60. For the second number 1/59, third 1/58, fourth 1/57, fifth 1/56. Multiply these together to get the chances of 5 winning numbers. There are 120 ways of arranging 5 numbers so, since order doesn't matter, we calculate: 120 times this chance =0.0000001831 approx (1 in 5,461,512). More to follow...

Answer 2

Continuation of answer (network failure prevented me from editing). Chances of not winning are 1 less this number=0.999999169. For 100 tickets we raise this to power 100=0.999981690 and subtract from 1 to get the chance of winning: 0.00001831.