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.