In a new lotto game, you must choose six numbers from the numbers 1 to 25.
Six winning numbers are drawn,
. . then one supplemental number is drawn from the remaining numbers.
You win Fifth Prize if your 6 numbers contain exactly 3 of the winning numbers
. . and the supplemental number.
Find the probability of winning Fifth Prize.
There are: . ways to choose the 6 numbers
. . and choices for the supplemental number.
Hence, there are: . possible outcomes.
To win Fifth Prize:
You must have 3 of the 6 winning numbers: . ways.
You must have the supplemental number: . way.
Your other two numbers are from the 18 "losers": . ways.
Hence, you have: . ways of winning.