Per (1 Viewer)

[juantheron]

How many ways there are to arrange the letter of the word "GARDEN" with the vowels in alphabet order.

 

[deswa1]

I just learnt perms and combs over the last few days so this might be wrong (someone correct me if I'm wrong) but here's how I'd do it:

We want the vowels in alphabetical order. Given any two spaces in this six letter word, we can obviously arrange the vowels alphabetically in one way (put the a in the first spot and the e in the second). We can choose two spaces out of 6 in 6C2 ways. Now we can arrange the other four letters in whatever way we want so the total arrangements are:

4!x(6C2)

 

[Carrotsticks]

There are two vowels, A and E.

The A is either before the E, or after the E.

So the number of ways in alphabetical order (A is before E) is the total, divided by 2.

6!/2

 

[deswa1]

There are two vowels, A and E.

The A is either before the E, or after the E.

So the number of ways in alphabetical order (A is before E) is the total, divided by 2.

6!/2

Haha yep this is an easier way than mine thanks Carrot. At least I got it right though - I think I'm slowly getting this topic

 

[RealiseNothing]

Just for creative sake:

You can also arrange the two vowels in alphabetical order first. This will always be the "total letters minus one" triangular number. There are 6 letters, so we take the 5th triangular number, ie 15.

Now the other 4 consonants can be arranged in 4! ways = 24 ways.

24 x 15 = 360 ways.

 

[juantheron]

Thanks friends got it