The selection of k object out of n, is done is C(n, k) many ways,
where, [tex]C(n, k)= \frac{n!}{k!(n-k)!} [/tex]
For example,
the selection of 2 objects out of 3, can be done in:
[tex]C(3, 2)= \frac{3!}{2!1!}= \frac{3*2*1}{2*1}=3 [/tex] many ways.
another example,
the selection of 2 objects out of 5 can be done in:
[tex]C(5,2)= \frac{5!}{2!3!}= \frac{5*4*3!}{2!*3!}= \frac{5*4}{2}=10 [/tex]
many ways.
back to our example,
there are C(3,2)=3 ways of selecting 2 boys out of 3, to form the 3 boys group together with Robert.
There are C(5,2)=10 many ways to select 2 girls out of 5.
Since any selection of the girls and boys can be combined, we have 3*10=30 different ways of forming the groups.
Answer: 30
