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In how many ways can the letters of word "EDUCATION&quo

This topic has 1 expert reply and 0 member replies

In how many ways can the letters of word "EDUCATION&quo

Post Thu Nov 09, 2017 12:15 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In how many ways can the letters of word "EDUCATION" be arraged such all the vowels always appear together?

    A) 9!
    B) 5!*4!
    C) 5!*5!
    D) 5!*4!*2!
    E) 6!*4!

    The OA is C.

    Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.



    Last edited by AAPL on Sat Nov 11, 2017 11:02 am; edited 1 time in total

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    Post Thu Nov 09, 2017 1:26 pm
    AAPL wrote:
    In how many ways can the letters of word "EDUCATION" be arraged such all the vowels always appear together?

    A) 9!
    B) 5!*4!
    C) 5!*5!
    D) 5!*4!*2!
    E) 6!*4!

    The OA is C.

    Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
    First, link the vowels together and treat them as a single letter, so we have E-U-A-I-O as one letter and then four more: D, C, T, N, giving us a total of 5 "letters." The number of ways that we can arrange 5 letters is simply 5!.
    But now we can also change the order of our vowels. There are five vowels, and therefore 5! ways that we could arrange those linked values.

    So there's 5! ways to arrange the five "letters" and 5! ways that we can arrange the linked vowels, giving us a total of 5!* 5! possibilities. The answer is C

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