Suppose there is a jar with $7$ balls: $4$ red, $2$ green and $1$ blue.
In how many unique ways can we choose $3$ balls?
Just by considering all the possibilities, I found out the answer is $6$. Namely:
- red, red, red
- red, red, green
- red, red, blue
- green, green, red
- green, green, blue
- blue, green, red
I was wondering if it is possible to express the solution in terms of the amount of different colors (in this case $3$) and the quantity per color. (in this case $4$, $2$ and $1$)