in how many ways can we distribute 6 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?
+118609 in how many ways can we distribute 6 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?
1:
The twins get 3 pecies each and the others get none. 1 Way
2:
The twins get 2 pieces each and one of the others gets 2 pieces 3 ways
The twins get 2 pieces each and 2 of the others get 1 piece 3 ways
3:
The twins get 1 piece each and one of the others gets 4 pieces 3 ways
The twins get 1 piece each and the others get 3,1, and 0 pieces 3!=6 ways
The twins get 1 piece each and the others get 2,2, and 0 pieces 3 ways
The twins get 1 piece each and the others get 2,1, and 1 pieces 3 ways
4.
The twins get 0 and one of the others gets 6 pieces 3 ways
The twins get 0 and the others get 5,1, 0 6 ways
The twins get 0 and the others get 4,2, 0 6 ways
The twins get 0 and the others get 4,1, 1 3 ways
The twins get 0 and the others get 3,3, 0 3 ways
The twins get 0 and the others get 3,2, 1 6 ways
The twins get 0 and the others get 2,2, 2 1 ways
So that is 1+3+3+3+6+3+3+3+6+6+3+3+6+1 = 50
I could easily have made a careless mistake but my logic is sound.
