4 letter word 1x2x3x4=24 (No. of arrangements)
(all different)
5 letter word 1x2x3x4x5=120
(all different)
6 letter word 1x2x3x4x5x6=720
(all different)
I then finished off the table up to a 10-letter word (all different letters).
Next I decided to do a further investigation, to investigate the number of different arrangements of words where 2 letters are the same.
Take the word aabb (4 letters, 2 different).
aabb has six different arrangements:
- aabb
- abab
- abba
- baab
- bbaa
- baba
There are 3 arrangements beginning with a and 3 arrangements beginning with b.
In a 4-letter word (all letters different) there are 24 arrangements, 6 beginning with each letter. The formula for this is the same for a 4-letter word but it must be divided by the number of a’s and the number of b’s in the word.
i.e. 4-letter word / 2a’s x 2b’s = No. of arrangements
1x2x3x4 / 1x2 1x2 = 24/4 = 6
The same formula goes for a 5 letter word (2 different letters). Take the word aaabb:
5 letter word / 3a’s x 2b’s = No. of arrangements
1x2x3x4x5 /1x2x3 x 1x2 = 120/12 = 10
I have now produced a table for words with 2 different letters.
To further my investigation I have decided to investigate words with 3 different letters. First I will try to find the number of arrangements for the word abc using the formula then I will check it is correct by working it out myself, if the 2 results are the same then I will carry on finding the number of arrangements for words with 3 different letters in and produce a table.
3 letter word / 1a x 1b x 1c = No. of arrangements
1x2x3 /1x1 x 1x1 x 1x1 = 6/1 = 6
- abc
- acb
- bca
- bac
- cab
- cba
Both methods produced the same number of arrangements (6).
