Quote:
Originally Posted by whosnext
My approach is to carefully list all the possible cases (mutually exclusive and collectively exhaustive). It is typically straightforward to tally each case at that point.
For your question, my list of cases would be:
1. {2,3} are both singletons
2. {2,3} is one pair and one singleton
3. {2,3} are both pairs
4. {2,3} is one trips and one singleton
5. {2,3} is one trips and one pair
6. {2,3} is one quads and one singleton
I tallied these cases and got a total that I'd be happy to share if you want.
1. C(4,1)*C(4,1)*C(24,3) = 32,384
2. C(2,1)*C(4,2)*C(4,1)*C(24,2) = 13,248
3. C(4,2)*C(4,2)*C(24,1) = 864
4. C(2,1)*C(4,3)*C(4,1)*C(24,1) = 768
5. C(2,1)*C(4,3)*C(4,2) = 48
6. C(2,1)*C(4,4)*C(4,1) = 8
TOTAL = 47,320