Question 332750
Let's pick from type A first.
We need to pick 4.
First pick has 6 choices
Second one now has 5
Third 4
Fourth 3
That leaves 2 extra type As
Now let's pick 4 from type B
Fifth pick has 7 choices
Sixth has 6
Seventh 5
Eight 4
That leaves 3 more type B.
We have two more picks to make and 5 question left to pick from
Ninth has 5 choices
Tenth has 4

Now, do the math
{{{6*5*4*3 * 7*6*5*4 * 5*4}}}
Solve that and there you go!