# permutation help! (1 Viewer)

#### DAFUQ

##### Member
1) Since you want the letters of KOALA in order, fix those first:
__ K __ O __ A __ L __ A __
The lines indicate the spots the letters of GUMTREE can be placed

2) Choose the spot for the letter G: 6 spots means 6 ways to do so. Then our arrangement becomes something like (depending on your spot for G):
__ K __ O __ A __ L __ G __ A __

3) Choose the spot for the 2nd letter: Now there are 7 spots and hence 7 ways to do so. Then our arrangement becomes something like:
__ K __U __ O __ A __ L __ G __ A __

Continue this above pattern for each letter of GUMTREE, and then dividing by 2 since the letter E is repeated, we get the number of ways to be: 6*7*8*9*10*11*12/2=1995840
i think thats the simplest method ive seen so far. +1 like

#### 4025808

##### Well-Known Member
1) Since you want the letters of KOALA in order, fix those first:
__ K __ O __ A __ L __ A __
The lines indicate the spots the letters of GUMTREE can be placed

2) Choose the spot for the letter G: 6 spots means 6 ways to do so. Then our arrangement becomes something like (depending on your spot for G):
__ K __ O __ A __ L __ G __ A __

3) Choose the spot for the 2nd letter: Now there are 7 spots and hence 7 ways to do so. Then our arrangement becomes something like:
__ K __U __ O __ A __ L __ G __ A __

Continue this above pattern for each letter of GUMTREE, and then dividing by 2 since the letter E is repeated, we get the number of ways to be: 6*7*8*9*10*11*12/2=1995840
Probably the best sort of thinking to approach this Q. Just make sure your answer is right too. +1

#### DAFUQ

##### Member
Probably the best sort of thinking to approach this Q. Just make sure your answer is right too. +1
it should be right because i also did it with a different method

#### 4025808

##### Well-Known Member
it should be right because i also did it with a different method
Oh okay, well we'll see what the answer says. OP, what's the answer?

#### john-doe

##### Member
And the answer is 1995840 !!!!! Thanks everyone!!!!!!!

#### raymondkp

##### New Member
And the answer is 1995840 !!!!! Thanks everyone!!!!!!!
Hi

There are 12! with all letters.
There are 5! ways of Koala
DIVIDE! (This brings back to only 1 of the KOALA variations.
Then divide by 2 for the "EE"
Cheers

#### Roy G Biv

##### Member
1) Since you want the letters of KOALA in order, fix those first:
__ K __ O __ A __ L __ A __
The lines indicate the spots the letters of GUMTREE can be placed

2) Choose the spot for the letter G: 6 spots means 6 ways to do so. Then our arrangement becomes something like (depending on your spot for G):
__ K __ O __ A __ L __ G __ A __

3) Choose the spot for the 2nd letter: Now there are 7 spots and hence 7 ways to do so. Then our arrangement becomes something like:
__ K __U __ O __ A __ L __ G __ A __

Continue this above pattern for each letter of GUMTREE, and then dividing by 2 since the letter E is repeated, we get the number of ways to be: 6*7*8*9*10*11*12/2=1995840
wow, this is brilliant!