adamtj

11-19-2015, 01:22 PM

Hello, I am hoping this is in the right sub group please do let me know if I chose incorrectly.

So I have part of this solved ( I think)

The basics:

Total population of objects :20

slots to fill: 5

total population of sets: 3.2MM (20^5)

My goal is to organize this total population into groups.

aaaaa - 5 of a kind

aaaab - 4 of a kind, 1 single

aaabb - 3 of a kind, 1 pair

aaabc - 3 of a kind, 2 singles

aabbc - 2 pairs, 1 single

aabcd - 1 pair, 3 singles

abcde - all singles

so using nPr I came up with the following:

category-count

aaaaa-20

aaaab-380

aaabc -6,840

aaabb-380

aabbc -6,840

aabcd -116,280

abcde -1,860,480

This is incomplete as it sums to 1,991,220.

the next step as I was seeing it was that there are variations of each category:

Example: aaaab,aaaba,aabaa and so on.

the plan was to calculate the permutations for each and then multiplying that by the initial calculations. but this yields much too large a population. so now I am stuck.

Here is the google sheets document I have been working with:

https://docs.google.com/spreadsheets...it?usp=sharing (http://mathhelpboards.com/redirect-to/?redirect=https%3A%2F%2Fdocs.google.com%2Fspreadsh eets%2Fd%2F1yrWacgebsqIsOwsofIR_sNjHG5FdlLs3VOJE7s 4DRDA%2Fedit%3Fusp%3Dsharing)

Any hints and help are greatly appreciated!

So I have part of this solved ( I think)

The basics:

Total population of objects :20

slots to fill: 5

total population of sets: 3.2MM (20^5)

My goal is to organize this total population into groups.

aaaaa - 5 of a kind

aaaab - 4 of a kind, 1 single

aaabb - 3 of a kind, 1 pair

aaabc - 3 of a kind, 2 singles

aabbc - 2 pairs, 1 single

aabcd - 1 pair, 3 singles

abcde - all singles

so using nPr I came up with the following:

category-count

aaaaa-20

aaaab-380

aaabc -6,840

aaabb-380

aabbc -6,840

aabcd -116,280

abcde -1,860,480

This is incomplete as it sums to 1,991,220.

the next step as I was seeing it was that there are variations of each category:

Example: aaaab,aaaba,aabaa and so on.

the plan was to calculate the permutations for each and then multiplying that by the initial calculations. but this yields much too large a population. so now I am stuck.

Here is the google sheets document I have been working with:

https://docs.google.com/spreadsheets...it?usp=sharing (http://mathhelpboards.com/redirect-to/?redirect=https%3A%2F%2Fdocs.google.com%2Fspreadsh eets%2Fd%2F1yrWacgebsqIsOwsofIR_sNjHG5FdlLs3VOJE7s 4DRDA%2Fedit%3Fusp%3Dsharing)

Any hints and help are greatly appreciated!