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Permutations (wrong section before)

  1. Nov 28, 2005 #1
    I've been told that this thread should have been in this section.


    Sorry about that.


    This is mind boggling.

    There is an array of 16 squares, arranged in a 4 x 4 grid. A supply of 4 A's, B's, C's, and D's are given. How many distinguishable ways are there of placing each of the letters in a square, if, one letter must appear once in each row and each column?

    I'm lost. There are 4! ways of placing the letters in the first row. But then when you get to the second row, you can place the A, which has 3 possible locations. But then the B, depends on where the A was placed. If the A was placed under the B in row 1, then you have 3 possible spots left, but if the A was placed under the C, then there are only 2 spots left. Shown below.

    The letters represent their placement, the 0 represents a spot that a B can't be placed, and a - represents a spot the B CAN be placed.
    R1: ABCD
    R2: -A--


    R1: ABCD
    R2: -0A-

    See the problem? How do I get around this????
    Last edited: Nov 28, 2005
  2. jcsd
  3. Nov 28, 2005 #2

    matt grime

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    Homework Helper

    YOu might want to cut and paste the text, it;ll be easier to answer in this forum if the question is here.
  4. Nov 28, 2005 #3
    Ok, I thought about another way I might be able to do this.

    I'm assuming that for ever arrangement of the 4 A's, there is an arrangement for the other letters that works.

    There are 4 ways of placing the A in the first row, 3 in the second, 2 in the third, and 1 in the last, making 24 arrangements of the A placement.

    For each of these there are 3 other arrangements possible, for the other 3 letters. So are there 24*3 ways of arranging the letters?
  5. Nov 28, 2005 #4
    Ok, so the question is edited into the first post above. If somebody could post the method/answer they got it would be greatly appreciated as I have about 3 different answers on pieces of paper scattered in front of me, and its due tomorrow:surprised
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