Combination on grouping On a college baseball squad, there are $3$ catchers, $5$ pitchers, $7$ infielders, $7$ outfielders. How many different baseball nines can be formed?
Since the question asked $9$ players , I thought the answer would be ${}^{22}\mathrm C_9$. But I am still having doubt with my answer teachers.
 A: I suspect this is a question where you need to know more about baseball rather than more about combinatorics! Does a "baseball nine" have some restrictions on how many of each type of player there can be? 
I don't understand baseball, but have googled it. (If someone more knowledgeable is reading, please let me know whether what follows is correct.) Based on that I assume a "nine" is a set of players capable of filling the nine positions: one catcher, one pitcher, four different infield positions and three different outfield positions. I don't know whether you're supposed to interpret two "nines" as being the same if they consist of the same nine players, or whether every player has to be in the same position.
Based on this, can you see how many "nines" there are under the two interpretations: same nine players, i.e. order within the two larger groups doesn't matter; and same positions, i.e. order does matter?
A: The figures give people capable of playing in types of positions. From them compute possible number of distinct teams of $9$ ($1$ catcher, $1$ pitcher, $4$ infield, $3$ outfield) that can be formed.
Thus # of possible teams = $\binom31\binom51\binom74\binom73 = 18,375$
