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datatable - How do you present a table (and graph) illustrating frequencies by permutation group sizes in R?

I'm trying to work out how to illustrate in a table and graph, the frequencies (numbers of groups) by permutation group sizes of my data.

My data consists of 8 variables (dog breeds) assigned, 'my_col', with 3 levels (colours) assigned, 'my_lev'. I have generated a random dataset with 50,000 outputs. So far I have calculated there are 6,557 possible unique rows (i.e. permutations of category levels).

As this is a random dataset, there are some similar rows of data, as indicated by the COUNT in this snapshot table;

df[, .(COUNT = .N), by = names(df)]

    Poodle Labrador   Pug Chihuahua Collie Shitzu Bulldog Lurcher COUNT
1:  brown    brown black     black  brown  white   black   white     8
2:  black    white brown     white  black  brown   brown   brown     7
3:  white    black brown     brown  black  black   black   black     6
4:  brown    brown brown     brown  brown  black   black   white    11
5:  brown    black black     black  white  white   brown   white    10
---
6553:  brown    black white     black  brown  white   black   brown     3
6554:  brown    black white     white  white  brown   black   white     1
6555:  brown    black white     white  brown  black   brown   black     1
6556:  black    white brown     brown  black  white   black   black     1
6557:  white    white white     black  brown  white   brown   white     1

I would like to end up with a new table with 2 headings, 'Group Size' and 'No. of Groups'.

How do I calculate how many groups are unique combinations (group size = 1), how many groups are made up of a pair of matching combinations (group size = 2), how many groups are made up three the same, etc?


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