Question

A lottery game is set up so that each player chooses six different numbers from 1 to 15. If the six numbers match the six numbers drawn in the lottery, the player wins (or shares) the top cash prize. What is the probability of winning the prize with 50 different lottery tickets?

Answer 1

we assume that order does not matter right?

Answer 2

there are chosen 6 15 digit numbers
by the counting principle there are \(15^6\) possible equally likely outcomes

Answer 3

you have six numbers, and if order doesn't matter there are \(6!\) ways to arrange them, so the probability you win on a ticket i believe is
\[\frac{6!}{15^6}\] and amazingly small number

Answer 4

Thank you so much!