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Distribution of Mean of the Combinations of a Set.

For some purpose
I found myself generating and analyzing the average of the combinations
of a set and when I generated the corresponding histogram I was
surprised by its shape.

It should be
remembered that the combinations C(m, n) of a set are the number of
subsets of a set of m elements taken from n in n.
The number of combinations is calculated with:
This is the very simple code to generate the combinations, calculate their mean and generate the histogram:
**m <- 50**

n <- 6

**COMBINATIONS <- t(as.data.frame(combn(m,n)))**

C_M <- apply(COMBINATIONS, 1, mean)

hist_all <- hist(C_M, breaks = length(unique(C_M)), col = "blue")

Interesting histogram. It's as if there are two distributions.
But if we change the value of n by:
**m <- 50**

n <- 4
We obtain the following histogram:
Although it is a
very simple math and programming exercise, the interesting thing is to
interpret why histograms behave this way, so it becomes an exercise in
understanding the visualization.
https://github.com/pakinja/Data-R-Value