A committee, which consists of two mathematicians and three scientists, will be formed from four mathematicians and six scientists. How many possible committees can be formed if :

Question

a. any of the mathematicians and scientists are included?
b. one particular scientist must be in the committee?
c. two particular mathematicians must be int he committee?
d. two particular scientists must not be int he committee?

Answer 1

a) number of (2math, 3 science() = C(4,2) x C(6,3) =120
b) one specific scientist must be in, so need 2 other scientist
= C(4,2) x C(6,2) = 90
c) 2 specific math guys must be in, but we need only 2 maths, so only need the 3 science
= C(6,3) = 20

d) 2 specific science guys are out, so need 3 from remaining 4 science guys
= C(4,2) x C(4,3) = 24