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

nari

New member
Mar 4, 2018
4
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
Feb 7, 2012
2,681
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
Mar 4, 2018
4
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?
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,031
So then the options would be: eo/oe + r o/e c k t?
I don't quite follow the whole logic here but the beginning part is true, the letter pairs are "eo" or "oe". For simplicity let's just called these two letters P (for pair). Opalg suggested the same thing but maybe seeing it like this will help.

How many ways can you arrange RPCKT?