Perms and Combs (1 Viewer)

[HeroWise]

Its the Gumtree Koala question from cambridge

It says "If the letters of GUMTREE and the letters of the word KOALA are combined and arranged into a single 12 letter word how many arrangements have KOALA in the correct order"

I got 11!/2! which is 19958400
Answer is 1995840

Its got one less zero LOL can someone explain how theyd do it with stars and bars or anyother alternatives

EDIT: Never mind figured it is it 12!/5!2! ?

 

[BenHowe]

The bit you need to read properly is that "KOALA in the correct order". This doesn't imply that KOALA is adjacent, rather K__O_A_L_A___ etc. Try accounting for this.

 

[fan96]

Your second answer is correct.

First, suppose we are adding 5 X's to GUMTREE.

(These X's will represent the letters of KOALA which we will deal with later)

There are unique arrangements this way.

For each of these arrangements there is exactly one way the X's can be replaced with the letters of KOALA - because the letters must appear in order.

 

[HeroWise]

How i did it was like, 5 bars and 7 stars
12!/(5! 2!)

5! for KOALA reduction and 2! for the double Es