I found that when you multiply the no. of letters by the previous amount of permutations, you will find the correct amount of permutations.
To find out how many permutations there are in a 3-letter word: 3*2 = 6 (which is 3!)
To find out how many permutations there are in a 4-letter word: 4*6= 24 (which is 4!)
I also noticed that each no. of permutations is equal to how many letters there are factorial.
Therefore,
To find out how many permutations there are in a 2-letter word: 1*2 = 2!
To find out how many permutations there are in a 3-letter word: 1*2*3 = 3!
To find out how many permutations there are in a 4-letter word: 1*2*3*4 = 4!
This shows that a formula for the number of permutations in a name that has different letters is n! (n = no. Of letters)
Therefore, for a 5 letter word with 5 different letters there will be 120 permutations.
Therefore, for a 6 letter word with 6 different letters there will be 720 permutations.
Therefore, for a 10 letter word with 10 different letters there will be 3628800 permutations.
Therefore,
I am now going to test weather duplicates of letters will make a difference in the no. of permutations.
3 LETTER NAME
WITH 2 LETTERS THE REPEATED
BOB
- BOB
- BBO
- OBB
4 LETTER NAME
WITH 2 LETTER THE REPEATED
EMMA
- EMMA
- EMAM
- EAMM
- MEMA
- MEAM
- MMEA
- MMAE
- MAME
- MAEM
- AEMM
- AMEM
- AMME
4 LETTER NAME
WITH 3 LETTERS THE REPEATED
LILL
- LILL
- ILLL
- LLIL
- LLLI
5 LETTER NAME
WITH 2 LETTERS THE REPEATED TWICE
EDDIE
- EDDIE
- EDDEI
- EDIDE
- EDIED
- EDEID
- EDEDI
- EIEDD
- EIDDE
- EIDED
- EEIDD
- EEDID
- EEDDI
- DDIEE
- DDEIE
- DDEEI
- DEDIE
- DEDEI
- DEIDE
- DEIED
- DIEED
- DIEDE
- DIDEE
- DEEID
- DEEDI
- IEEDD
- IDDEE
- IDEDE
- IDEED
- IEDED
- IEDDE
5 LETTER WORD WITH 3 LETTERS REPEATED
DADDY
- DADDY
- DDDAY
- DDDYA
- DDADY
- DDAYD
- DADYD
- ADDDY
- ADDYD
- ADYDD
- AYDDD
- YDDDA
- YDDAD
- YDADD
- YADDD
- DDYAD
- DDYDA
- DAYDD
- DYADD
- DYDAD
- DYDDA
To make it easier I will now use X’s &Y’s (any letters)
3 letters
XXY
- XXY
- XYX
- YXX
4 LETTERS
XXXY
- YXXX
- XYXX
- XXYX
- XXXY
5 LETTERS
XXXXY
- XXXXY
- XXXYX
- XXYXX
- XYXXX
- YXXXX
I found:
For 3 letters with 2x’s & 1y the no. Of permutations are divided by 2 (which is 2!), after using the formula for completely different letters.
For 4 letters with 3x’s & 1y the no. Of permutations are divided by 6 (which is 3!), after using the formula for completely different letters.
For 5 letters with 4x’s & 1y the no. Of permutations are divided by 24 (which is 4!), after using the formula for completely different letters.
This shows another pattern of factorial.
Therefore you need to divide the number of letters factorial by the number of x’s factorial. This leaves me with:
N!
X!
Using this I know that:
5x’s & 1y would make 6 combinations
6x’s & 1y would make 7 combinations
But I also predict that if you add in extra Y’s as well the no. Of permutations changes once again.
4 LETTERS
XXYY
- XXYY
- XYXY
- XYYX
- YYXX
- YXYX
- YXXY
5 LETTERS
XXXYY
- XXXYY
- XXYXY
- XXYYX
- XYXYX
- XYXXY
- XYYXX
- YYXXX
- YXYXX
- YXXYX
- YXXXY
For 4 letters with 2x’s & 2y’s after using the formula N! , that no. of
X!
permutations was divided by 2 (which is 2!) to find the number of permutations.
For 5 letters with 2x’s & 3y’s after using the formula N! , that no. of
X!
permutations was divided by 6 (which is 3!) to find the number of permutations
This shows another pattern of factorial.
Therefore you need to divide the formula by Y!. This now becomes:
N!
X! *Y!
Now using this formula I will be able to determine the no. Of permutations in any name or letter combination.
Using my formula I can prove how many permutations are in these names
Now I will find out the no. Of permutations using x’s & y’s
