Formula for the number of all combinations of  things, taken  at time is  .

players who can only play catcher :

Find the combinations of players taken at a time.

Substitute in .

.

players who can only play first base:

Find the combinations of players taken at a time.

Substitute in .

.

players who can only pitch:

Find the combinations of players taken at a time.

Substitute in .

.

players who can play in any of the remaining positions:

Find the combinations of players taken at a time.

Substitute in .

.

Find the number of -player teams that can be made:

The Fundamental Counting Principle :

Number of teams

                            .

Number of teams = .