I have asked a similar question here and answers were very helpful. I tried doing similar questions and could solve them comfortably. However, I myself came up with a question like this and wondering how to solve this.
Suppose there are 20 black balls, 10 yellow balls and 5 brown balls. Balls of same color are identical. Order of selection does not matter.
- How many ways can a selection of 15 balls be made?
- How many ways can a selection of 15 balls be made if 2 brown must be selected always?
(1) number of solutions of $x_1+x_2+x_3 = 15$ with $0\le x_1\le 20; 0 \le x_2 \le 10; 0 \le x_3 \le5$ is the solution. Is this right? if so, is there any formula for this?
(2) Select the 2 brown balls in (only 1 way) and then find number of solutions of $x_1+x_2+x_3 = 13$ with $0\le x_1\le 20; 0 \le x_2 \le 10; 0 \le x_3 \le3$
Please give directions on how to approach similar problems. thanks.