GalwayMathsStudent
New member
- Joined
- Sep 14, 2016
- Messages
- 3
The question first says put 20 indistinguishable objects into 4 groups. How many ways can this be done?
This part was pretty easy ( I think) I just used the formula (n+r-1)c(r-1) and got the answer 1771.
The second part asked How many ways if not all objects need to be put in a group?
I am pretty sure this is just the sum from 1 to 20 indistinguishable objects into 4 groups.
After some manipulation I got it down to =(1/6) sum (from k=1 to 20){ ((3+k)!)/(k!)}
which I then simplified to = (1/6) sum (from k=1 to 20) {k^3+6k^2+11k+6}
I just can't see a way to get an answer fast. Sure I could just add 20 values from my calculator but I feel like I am missing some shortcut or easier approach to this problem.
Any Feedback would be appreciated
This part was pretty easy ( I think) I just used the formula (n+r-1)c(r-1) and got the answer 1771.
The second part asked How many ways if not all objects need to be put in a group?
I am pretty sure this is just the sum from 1 to 20 indistinguishable objects into 4 groups.
After some manipulation I got it down to =(1/6) sum (from k=1 to 20){ ((3+k)!)/(k!)}
which I then simplified to = (1/6) sum (from k=1 to 20) {k^3+6k^2+11k+6}
I just can't see a way to get an answer fast. Sure I could just add 20 values from my calculator but I feel like I am missing some shortcut or easier approach to this problem.
Any Feedback would be appreciated