library(partitions)
library(BiasedUrn)
# Sum probabilities for all combinations of two groups.
# Only works when length(x) = 3. We wish to merge x[1] and x[2].
sum.mFNCH<-function(x, m, s, w, prec = 1e-07){
  rr <- restrictedparts(sum(x[1:2]),(length(x)-1))
  ss <- 0
  for(i in 1:ncol(rr)){
    ss <- sum(ss, dMFNCHypergeo(c(rr[,i],x[3]),m,s,w, precision=prec) )
    ss <- sum(ss, dMFNCHypergeo(c(rev(rr[,i]),x[3]),m,s,w, precision=prec) )
    }
  return(ss)
  }

# Multi-variate probability for 3 ball groups with:
# 22, 47, and 139 balls and weights 0.1, 0.2, and 0.3.
# Sample a total of 7 balls for the first two groups and 15 for the third.
x <- c(2,5,15)
m <- c(22,47,139)
w <- c(0.1,0.2,0.3)
sum.mFNCH(x, m, sum(x), w, prec=1e-8)
[1] 0.1108098

# Univariate equivalent using average weight.
wr <- ((22/69)*0.1+(47/69)*0.2)
# Scale odds relative to third group which now constitute the white balls:
wr <- wr/0.3

dFNCHypergeo(7, 69, 139, sum(c(7,15)), wr)
[1] 0.1120066