A STATE LOTTERY IS DESIGNED SO THAT A PLAYER CHOOSES FIVE NUMBERS FROM 1 TO 30 ON ONE LOTTERY TICKET. WHAT IS THE PROBABILITY THAT A PLAYER WITH ONE TICKET WILL WIN? WHAT IS THE PROBABILITY OF WINNING IF 100 DIFFERENT TICKETS ARE PURCHASED?

Answer 1

Number of possible combinations of 5 (distinct) numbers out of 30
= 30C5
Probability of winning if n different tickets are bought
= n/(30C5)

where 30C5
=30!/((30-5)!5!)