Indistinguishable Objects to Distinguishable Boxes

# Indistinguishable Objects to Distinguishable Boxes

# The number of different ways to distribute Nballs indistinguishable balls into

# Nboxes distinguishable boxes is C(Nboxes+Nboxes-1,Nboxes-1).

# For example, 5 balls into 3 boxes can be done in these C(7,2) = 21 ways:

# Number of balls

Nballs <- 10

# Number of boxes

Nboxes <- 3

# The number of different ways to distribute n indistinguishable balls into

# k distinguishable boxes is C(n+k-1,k-1).

# nb<-choose(N+nbjour-1,nbjour-1)=dim(tb)[1]

# divers<-matrix(rep(0, nbjour*nb), ncol=nbjour)

# generate all possible positions of the boundaries

xx <- combn(Nballs+Nboxes-1, Nboxes-1)

# compute the number of balls in each box

a <- cbind(0, diag(Nboxes)) - cbind(diag(Nboxes), 0)

tb <- t(a %*% rbind(0, xx, Nballs+Nboxes) - 1)