How many ways can I select Ralf when I do not select Mabel?

Question

Ok there are 6 guys and 7 girls and I need to order them in 4 positions. I am guessing that I have to use nCr but I am not sure how to do this.

Answer 1

Excluding Mable, you have
12*11*10*9 = 11,880
permutations. There are
11*10*9*8 = 7,920
of those, the permutations which do not have Ralf in them
11,880 - 7,920 = 3,960
permutations which can have Ralf but not Mabel The total permutations for the full group is
13*12*11*10 = 17,160,
so the probability that you select Mark and not Mabel is
3,960/17,160 = 0.2307692,
but the probability of selecting Ralf when Mable has already been excluded is
3,960/11,880 = 0.3333333, or 1 in 3

Answer 2

I am guessing that you are trying to pick a team of 4 from the 6 boys and 7 girls. If there are no restrictions then you have

13C4

If you need two boys and two girls then 6C2 * 7C2.

Depending on your restrictions, you can use this idea to construct any kind of team you like from the group of boys and girls.