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Math Help - Noughts and Crosses arrangement

  1. #1
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    Noughts and Crosses arrangement

    12 noughts and 4 crosses are arranged in 4 rows of 4. For instance, one arrangement is:

    00x0
    0x0x
    0000
    x000

    i) How many arrangements are there?

    ii) How many arrangements with a cross in every row?

    iii) How many arrangements are there in which there is a cross in every row and in every column?

    So these are my answers, I wanted to check if they are correct:

    i) 16C4 = 1820

    ii) 4^4 = 256

    iii) 4! = 96

    I used the approach that there are 4 places to put the cross in the first column, then 3 in the 2nd, 2 in the 3rd, and 1 in
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  2. #2
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    Quote Originally Posted by Aquafina View Post
    12 noughts and 4 crosses are arranged in 4 rows of 4.
    i) How many arrangements are there?
    ii) How many arrangements with a cross in every row?
    iii) How many arrangements are there in which there is a cross in every row and in every column?

    So these are my answers, I wanted to check if they are correct:

    i) 16C4 = 1820

    ii) 4^4 = 256

    iii) 4! = 96
    Well done. They are correct.
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