WinterGraschp
New member
- Joined
- Mar 11, 2015
- Messages
- 3
Into how many distinct, equally sized (8 per group) groups can 32 unique cards be sparated, if 4 of those cards have to be together (eg. in the same group).
My solution was that first we make a set with 4 elements out of 28, because that is the set in which those 4 cards go, then we make a set with 8 elements out of 24, then a set with 8 elements out of 16 and then finally a set of 8 elements out of 8 elements (which is 1). We multiply these so we got something like: (28|4) * (24|8) * (16|8) * (8|8), now this would be correct if the order of the groups would matter, but it doesn't so we divide the whole thing with 4!, because there are 4 groups so we finally get: ((28|4) * (24|8) * (16|8) * (8|8)) / 4!
Now apparently my soulution is fine, except for the fact that we have to divide by 3!, according to the solution.
I'm either right and the solution provided is wrong, or they are right and i have no idea why.
Please help!
My solution was that first we make a set with 4 elements out of 28, because that is the set in which those 4 cards go, then we make a set with 8 elements out of 24, then a set with 8 elements out of 16 and then finally a set of 8 elements out of 8 elements (which is 1). We multiply these so we got something like: (28|4) * (24|8) * (16|8) * (8|8), now this would be correct if the order of the groups would matter, but it doesn't so we divide the whole thing with 4!, because there are 4 groups so we finally get: ((28|4) * (24|8) * (16|8) * (8|8)) / 4!
Now apparently my soulution is fine, except for the fact that we have to divide by 3!, according to the solution.
I'm either right and the solution provided is wrong, or they are right and i have no idea why.
Please help!