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Math Help - 2 objects to be filled into 3 spaces

  1. #1
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    2 objects to be filled into 3 spaces

    The letters 'P, I, H, A, T ' are to be arranged in a row. Find the number of possible arrangement if the vocals letters occupy the even position


    after filling in P, H , T into second and fourth location, now there's only 2 letter (I and A ) , to be filled into 2 locations. how to do this? 2 objects to be filled into 3 spaces-er.png
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  2. #2
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    Re: 2 objects to be filled into 3 spaces

    Quote Originally Posted by delso View Post
    The letters 'P, I, H, A, T ' are to be arranged in a row. Find the number of possible arrangement if the vocals letters occupy the even position


    after filling in P, H , T into second and fourth location, now there's only 2 letter (I and A ) , to be filled into 2 locations. how to do this? Click image for larger version. 

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    I don't understand what you've written. You seem to be putting 3 letters into 2 slots.

    Assuming the slots are 1-5 there are 2 even positions, 2 and 4.

    There are only 2 ways to put the "vocals letters" (a better English word is vowels) into these slots. I=2, A=4; or A=2, I=4.

    Then there are 3! ways of arranging the consonants (the remaining letters).

    2*3! = 12

    so there are 12 arrangements that have vowels in even numbered slots.
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  3. #3
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    Re: 2 objects to be filled into 3 spaces

    Hello, delso!

    The letters 'P, I, H, A, T ' are to be arranged in a row.
    Find the number of possible arrangement if the vowels occupy the even positions.

    After filling in P, H, T into second and fourth location. . .
    HOW did you fit three letters into two positions?

    \text{We have: }\;\_\;\_\;\_\;\_\;\_

    \text{Place the two vowels: }\;\_\;\text{v}\;\_\;\text{v}\;\_
    There are 2! permutations of the vowels.

    \text{Place the three consonants: }\:\text{c}\;\text{v}\;\text{c}\;\text{v}\;\text{c  }
    There are 3! permutations of the consonants.

    Therefore, there are: . (2!)(3!) \,=\,12 possible arrangements.
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