# How many ways can all the letters in the word ROCKET be arranged so that the vowels are always together?

#### nari

##### New member
Hi! There is this question in my practice exam:

How many ways can all the letters in the word ROCKET be arranged so that the vowels are always together?

The answer is 5! x 2.

I understand where the 2 is coming from. What I don't understand is the 5. Shouldn't it be 4!, since we already selected two out of six letters?

#### Opalg

##### MHB Oldtimer
Staff member
Hi! There is this question in my practice exam:

How many ways can all the letters in the word ROCKET be arranged so that the vowels are always together?

The answer is 5! x 2.

I understand where the 2 is coming from. What I don't understand is the 5. Shouldn't it be 4!, since we already selected two out of six letters?
Think of the E and the O as being glued together. They then count as a single "letter", and you have 5! ways of arranging the five letters R OE C K and T. The 2 just tells you whether the E comes before or after the O.

#### nari

##### New member
Think of the E and the O as being glued together. They then count as a single "letter", and you have 5! ways of arranging the five letters R OE C K and T. The 2 just tells you whether the E comes before or after the O.
So then the options would be: eo/oe + r o/e c k t?