[jay_shark]

Here is an example .

If you want to know the number of ways of selecting 3 kids from 10 , the total number of ways this can occur is c(10,3) .If you care about the order in which you select them , then it is p(10,3) . Since in your example , we don't care about the specific order in which you select marbles so we use the C notation . In general C(x,z) is the number of ways of selecting z marbles from a bowl containing x . We must specify that x>=n for this to make any sense .

Since there are y red marbles in a bowl containing x marbles in total , it must be true that there are x-y non red marbles . We must select z from x-y non red marbles, this is just C(x-y,z) . The denominator , which is the total number of ways of selecting z from x marbles is c(x,z) . The next step is to divide the number of favorable cases over the total number of cases .