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## Probability

The letters of the word PROMISE have to be arranged so that no two vowels come together. Find the number of arrangements.

I don't know the solution and look for help. Thank you.

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PROMISE has four consonants and three vowels.

1. Arrange the consonants like this:

_ C _ C _ C _ C _

As you can see, there are four places for the consonants so they can be arranged in 4! ways.

2. To keep the vowels from being placed together, arrange them in the five _ spots around the consonants. Since there are only three vowels and five spaces, you can arrange them in 5P3 ways.

3. Multiply the two arrangements together.

4!*5P3=1440

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## Thank you

Thanks so much. It's much clear now.

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Hello,

i am starting my preparation for the GMAT right now and i generally i get the logic of the solution of the question, however i do not understand what the the "P" between 5 and 3 mean. Can you answer me please.

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I am sorry i asked before i tried to find it myself...everything is clear now. This is the right answer.

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