Solving a Practice Exam Question: Arranging Letters in ROCKET

In summary, the answer to the question of how many ways all the letters in the word ROCKET can be arranged so that the vowels are always together is 5! x 2. This is because the E and O are considered as a single "letter" and there are 5! ways to arrange the remaining letters. The 2 represents the different positions that the E and O can take within the pair. In other words, the options would be: P + RPCKT.
  • #1
nari
4
0
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?
 
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  • #2
nari said:
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.
 
  • #3
Opalg said:
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?
 
  • #4
nari said:
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?
 

FAQ: Solving a Practice Exam Question: Arranging Letters in ROCKET

How do I approach solving a practice exam question about arranging letters in ROCKET?

First, read the question carefully and make sure you understand what is being asked. Then, break down the word ROCKET into its individual letters. Next, determine how many ways those letters can be arranged using the formula n! (n factorial), where n is the number of letters in the word. Finally, use this information to solve the question.

Are there any tips or tricks for solving this type of question?

Yes, there are a few strategies that can make solving this type of question easier. For example, you can group the letters into categories (e.g. vowels and consonants) and then arrange them within those groups. You can also try solving smaller versions of the problem first, and then use that information to solve the larger problem.

How can I check my answer to make sure it is correct?

One way to check your answer is to use a permutation calculator or a combination calculator, which can generate a list of all the possible arrangements for a given set of letters. You can then compare your answer to this list to see if it matches.

What should I do if I get stuck on a particular part of the question?

If you get stuck on a particular part of the question, try breaking it down into smaller, more manageable parts. You can also try solving the question using a different approach or asking a friend or teacher for help. Sometimes, taking a break and coming back to the question with a fresh perspective can also be helpful.

How can I use this type of question to improve my overall problem-solving skills?

Solving practice exam questions about arranging letters in a word can help improve your problem-solving skills in a few ways. It can help you practice breaking down complex problems into smaller, more manageable parts. It can also improve your ability to think critically and use different strategies to approach a problem. Additionally, solving these types of questions can help improve your understanding of mathematical concepts such as permutations and combinations.

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