I am new to probability.
Please have a look at the following question.
We have n = 10 persons and we wish to divide them at random into 3 groups consisting of 5, 3, and 2 persons respectively. In how many ways is this possible?
I have tried to solve it in following way.
Total number of possible ways =
I think the above solution is correct but I really don't know how it happens.
I mean to say that I am confused in
1 - Why are we multiplying 10C5 with 5C3 and 2C2 ? Which rule or formula implies this multiplication of combinations?
2 - When and in which situations do I need to multiply combinations?
Any help would be highly appreciated.