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.
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.
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