Question 1083751
You will select 3 physicists out of 5: i.e  C(5,3) = 10 different ways
Then select 2 chemists out of 4: i.e, C(4,2) = 6 different ways
Lastly, one position will be filled by 1 out of 3 mathematicians, i.e 3
That is 10X6X3 =  180

But note: The question omitted a crucial word 'Different' in "....how many DIFFERENT ways can this be done"