- #1
moonbase
- 21
- 0
EDITED: Should be permutations not combinations
You have a bag of 10 marbles. There are 4 red marbles, 3 yellow, 2 green, and 1 blue marble. You remove them from the bag one of the time without replacement. Assuming each color of marble is identical and it doesn't matter which specific marble of each color is chosen, calculate the number of possible permutations in which you can remove the 10 marbles.
If the specific marble picked did matter, the answer would be 10! but I'm not sure how to apply the different odds of the colors.
I found the number of possible colors that can be picked for each draw.
1st: 4
2nd: 3, 4
3rd: 3, 4
4th: 2, 3, 4
5th: 2, 3
6th: 2, 3
7th: 1, 2, 3
8th: 1, 2
9th: 1, 2
10th: 1
Then I multiplied every possible value: (4*4)*(3*6)*(2*6)*(1*4)=13824
Am I doing this wrong? And is there a more efficient way to figure it out?
Homework Statement
You have a bag of 10 marbles. There are 4 red marbles, 3 yellow, 2 green, and 1 blue marble. You remove them from the bag one of the time without replacement. Assuming each color of marble is identical and it doesn't matter which specific marble of each color is chosen, calculate the number of possible permutations in which you can remove the 10 marbles.
Homework Equations
If the specific marble picked did matter, the answer would be 10! but I'm not sure how to apply the different odds of the colors.
The Attempt at a Solution
I found the number of possible colors that can be picked for each draw.
1st: 4
2nd: 3, 4
3rd: 3, 4
4th: 2, 3, 4
5th: 2, 3
6th: 2, 3
7th: 1, 2, 3
8th: 1, 2
9th: 1, 2
10th: 1
Then I multiplied every possible value: (4*4)*(3*6)*(2*6)*(1*4)=13824
Am I doing this wrong? And is there a more efficient way to figure it out?
Last edited: