Permutations and combinations. Picking a team A Football/Soccer team consists of $9$ players. $2$ wingers, $2$ midfielders, $2$ strikers and three defenders. (yes I know there's no Goalkeeper.)
The coach has $11$ wingers available to him, $7$ midfielders, $5$ strikers and $9$ defenders.
How many ways can the team be selected?
I know to pick the wingers there are 
$$ \frac{11!}{2!(11-2)!} \text{ways} $$
And the same goes for the rest of the positions
But how do i find the total number of ways to pick the entire team? Do I just sum them all?
Thanks in advance
 A: $${11 \choose 2}\cdot  {7 \choose 2}\cdot {5 \choose 2}\cdot {9 \choose 3}$$
You have to multiply them because, for example, for every choice of the wingers you have:
$${7 \choose 2}\cdot {5 \choose 2}\cdot {9 \choose 3}$$
possibilities for the rest of the team. 
And you can apply the same idea for the others positions.
A: You want to combine all possibilities into one big team arrangement. All selections (winger, midflier...) are independant one from another, so you should multiply them : the answer to your problem is ${11 \choose 2}\times{7 \choose 2}\times{5 \choose 2}\times{9 \choose 3}$

If you want to be convinced of it, just look at this small example.
I have 2 choices for my main plate, and 3 choices for my desert. How many different menus are there?
If I pick the first main plate, I have 3 choices for desert.
If I pick the second main plate, I have 3 choices for desert.
For every choice of main plate (and there are 2 of them), I have 3 choices for desert: I actually have $2 \times 3$ choices in total. Hence, multiplication is what you're looking for.
