# Libraries
using Combinatorics, StatsBase


# Settings
x     = ["H1", "T1", "H2", "H3"]
nflip = 3


# Calculate all permutations for nflip trials of the x possible outcomes
combs = collect(with_replacement_combinations(x, nflip))
perms = []
for i in eachindex(combs)
    perms = vcat(perms, collect(multiset_permutations(combs[i], nflip)))
end


# Count up the number of heads for each set of nflip trials
nheads = []
for i in eachindex(perms)
    perms[i] = replace.(perms[i], r"\d+" => "")
    nheads   = vcat(nheads, sum(perms[i] .== "H"))
end


# Aggregate results by number of heads
sort(countmap(nheads))
sort(proportionmap(nheads))