Investigate all the possible combinations there are of a person's name, using only the letters in their name.

From these results I know that a 4 letter name, with no repeated letters gives 24 possible combinations, my initial thoughts where that you simply times the number of letters by 6 to get the number of possible combinations.

I will be investigating this is Part 3

Part 2

Emma

In this section I will be exploring the possible combinations of a name that includes a double letter.

Possible Combinations:

1. emma
2. emam
3. eamm
4. meam
5. maem
6. mame
7. mema
8. mmea
9. mmae
10. amme
11. amem
12. aemm

From this we can see that there are 12 possible combinations of the name Emma. This could mean that to find the number of combinations in a name with repeated letters, you take the number of cominations in that amount of letters without repeated letters and divide it by to.

For example

24/2 = 12

As Lucy had 24 combination and when adding a double letter the number of combinations were 12.

I will investigate into this further in Part 3

Part 3 – Further Research

Rohan

I know from investigation that Rohan has 120 combinations of his name, and has 5 letters in his name.

There for it is 24 x 5.

24 was the amount of combinations in a 4 letter name.

There fore a 6 letter name would have 720 combinations as it would be 720/6

This pattern works.

Also a 2 letter name like Jo has combinations of

Jo

Oj

To find this we can do 1x2 which = 2!

There fore to find a 5 and 6 letter name we can do

5= 5x4x3x2x1 = 5! = 120

6=6x5x4x3x2x1 = 6! = 720

This formula also works and we have proved it with the name Rohan. As Rohan has 5 letters in his name, and using 5! = 120 and we know that is the amount of combinations

We use! as to find the number of combinations in a persons name we times the number of letters in their name by the number of combinations of a name with 1 less amount of letters.

So to find the combinations in a 6 letter name we take the amount in a 5 letter name (120) and times it by 6.

To get 120 you would of times 24 x 5.

This is 1x2x3x4x5 and then again x6 to get the combinations for Rohan.

General Formula

From this we can use X! as the general formula, where X= the number of letters in the name.

Emma

As Emma has a repeated letter the combinations are halved.

There fore the formula could be 4!/2

But with a name with 3 repeated letters this would not work.

The formula for a name with repeated letters is

X!/R! where R= the amount a letter is repeated.

Using this, the word ABCBDB would be

6!/3!

If a name has 2 sets of repeated letters then you simply divide it by the amount of repeated letters. So a name like Hannah would be

6!/2!2! as there are 2 A’s and N’s.

This is true of any word. For example ABACABCBACABA would be

14!/6!4!3!

Also from using ! we can easily work out all the combinations of a name without having to write them all out:

To test this table we can take 9!

Which is 1x2x 3x4x5x6x7x8x9 which is 362880