How many ways can you select 10 jellybeans from colors Red, Blue, Green so that at most you only have 4 Green jellybeans?
3. The Attempt at a Solution [/B]
# of ways = # of ways to pick 1 Green + # of ways to pick 2 Green + #of ways to pick 3 Green + # of ways to pick 4 Green.
1 Green jellybean: After picking out the jellybean, there are then 9 left to choose from.
* * * * $ * * * * *
If the '*' are the 9 jellybeans and '$' is the divider to separate the jellybeans so that those on the left of it are Red and those to the right of it are Blue then there are 10!/9! or 10 ways to rearrange it.
2 Greens: Following the same process above would result in 9!/8! = 9
3 Greens: 8!/7! = 8
4 Greens: 7!/6! = 7
Therefore you would have 10+9+8+7 ways to select 10 jellybeans with at most having 4 Green jellybeans.