Thread: Lotto Game

Rules of the Game:

1. Player selects 5 numbers 1-47.
2. Player selects a "special" number 1-27.
3. Five numbers are drawn and a special number is drawn.

What is the probability that the player matches three of five numbers and the special number?


Attempt:

I want to divide the "favorable" outcomes by the total number of possibilities. The total number of possibilities seems to be 47^5 X 27.

Now, the hard part seems to be the favorable outcomes. That is, how many combinations yield exactly 3 matches and 1 match with the special number?

Any help would be appreciated.

No, this involves combinations.

The possible number of outcomes with 5 numbers from 47 numbers is 47C5
Now, there is one more, number to pick out of 27, hence 27 possible ways

For a total of 27*47C5 possible combinations. (ie 41416353)

Now, for the favourable outcomes part:

Ways to get 3 matching numbers = 5C3 (3 good numbers from the 5 numbers which were drawn)

Then, the rest, being = 42C2 (ie, 2 of the 42 numbers not drawn)

And of course, there is only 1 out of 1 way to pick the good number.

For a total of 5C3 x 42C2 x 1

thanks my man!