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Math Help - Permutations Help...

  1. #1
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    Permutations Help...

    I have the word CATERING.
    I need to find out how many 5 letter words can be made using at least one vowel and one constant with repition.
    Thanks for any help.
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  2. #2
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    Hello, holmesb!

    A tricky one . . . It took a bit of Thinking.


    Given the word CATERING, how many 5-letter words can be made
    using at least one vowel and one consonant with repetition?

    With no restrictions, there are: .8^5 possible five-letter words.

    The only time we don't have at least one and one consonant
    . . is when we happen to pick five consonants.
    This can happen in: .5^5 ways.

    Therefore, the answer is: .8^5 - 5^5 .= .32,768 - 3,125 .= .29,643

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  3. #3
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    I had a go at this one earlier and thatís the answer I originally got. But then I thought what about the occurrences when 3 vowels and no constants are used as reputation is aloud. So I subtracted 3 ^5 from 29,643 to get 29, 400. I assume this is the correct answer as that it what is says in the text book. Thanks for your help anyway

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