Answer
See below.
Work Step by Step
If we want to choose $k$ elements out of $n$ disregarding the order, not allowing repetition, we can do this in $_{n}C_k=\frac{n!}{(n-k)!k!}$ ways.
The order doesn't matter here in the set of players, thus we have to use combinations.
Thus $_{10}C_{5}(linemen)\cdot_{10}C_{3}(linebackers)\cdot_{5}C_{3}=252\cdot120\cdot10=302400$