Let the people be {M1, M2, M3, M4, M5, W1, W2, W3, W4, W5}
where M1 is Man 1, W1 woman 1 and so on...
The formula [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex], gives the total numbers of ways of creating groups of r out of n.
r! means 1*2*3*...(r-1)*r.
The technical support group is going to have exactly 3 women, which will be chosen from 5 women, and 3 men which will be chosen from 5 men.
Each of the selections can be done in C(5, 3) many ways, and since the any selection of the men and women can be combined, in total there are:
C(5,3) *C(5, 3) many ways of creating the technical support group.
[tex]C(5,3) = \frac{5!}{3!2!}= \frac{5*4*3*2*1}{3*2*1*2*1}=10 [/tex]
10*10=100 many ways of forming the group.
Answer: 100
