Question

The baseball coach is going to pick 9 players for the team. He has 9 outfielders, 10 infielders, and 4 pitchers to pick from. The team must have 3 outfielders, 1 pitcher, and 5 infielders. How many ways can he select his baseball team? i dont know how to solve someone show me pls

Answer 1

The number of ways to select the team is the sum of the possible combinations of each category of player as follows:
\[9C3+ 4C1+10C5\]

Answer 2

THANK YOU SOOOOO MUCH, BUT WHAT'S AFTER THAT?

Answer 3

The formula for combinations is as follows:
\[\left(\begin{matrix}n \\ r\end{matrix}\right)=nCr=\frac{n!}{(n-r)!r!}\]
So taking the combinations of the 9 outfielders taken 3 at a time:
\[9C3=\frac{9!}{(9-3)!3!}=\frac{9!}{6!3!}=\frac{9\times 8\times 7}{3\times 2\times 1}\]
Can you finish the calculation for 9C3 ?