Question

JCL Computers has five vacancies in its executive trainee program. In how many ways can the company select five trainees from a group of fifteen female and fifteen male applicants if the vacancies
(b) Must be filled by two men and three women?

Answer 1

you are being asked how many ways to choose 2 out of 15 and 3 out of 15
do you know how to do that?

Answer 2

I thought it was 15*14 + 15*14*13
but its not

Answer 3

i.e. you are being asked for \[\binom{15}{2}\times \binom{15}{3}\] some times written as
\[_{15}C_2\times _{15}C_3\]

Answer 4

ok , it should be times, not plus, by the "counting principle" so one mistake the the plus sign

Answer 5

but another mistake is
\[\binom{15}{2}=\frac{15\times 14}{2}\] and
\[\binom{15}{3}=\frac{15\times 14\times 13}{3\times 2}\]

Answer 6

and again, it is times, not plus

Answer 7

if it was me, i would cheat rather than bother with a calculator or arithmetic
http://www.wolframalpha.com/input/?i=%2815+choose+2%29%2815+choose+3%29

Answer 8

thank you!!!