Question 896089
There are 3*2 = 6 ways to pick 2 chemists assuming order matters. Order doesn't matter though which means you have 6/2! = 6/2 = 3 ways to pick 2 chemists.


Put another way, there are 3 ways to NOT pick a chemist. 


-------------------------------------------------------


You have 5 slots. Two of these slots must be chemists. So you really have 5-2 = 3 slots left. 


You cannot have another chemist (that last third chemist) on the team because you must have *exactly* 2 chemists. No more and no less.


So you have 3 slots left and 7 people to choose from to fill those three slots.


-------------------------------------------------------


There are 7*6*5 = 42*5 = 210 ways to pick 3 people from a pool of 7


This is if order mattered. 


However, order doesn't matter, so you really have 210/3! = 210/6 = 35 ways to pick 3 people from a pool of 7.


-------------------------------------------------------


To sum up what we have so far:


We have 3 ways to pick two chemists
We have 35 ways to pick three physicists 


So there are 3*35 = <font size=4 color="red">105</font> ways to pick a team of five members.


Again, order does not matter.