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Math Help - Combinatorics question

  1. #1
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    Combinatorics question

    From a set of 12 flags, 4 blue,4 red, 2 green, 2 yellow,
    how many types of 12-flag signals are possible?

    Ans: 12!/ (4! 4! 2! 2!) = 207900

    Now what is the answer for 10-flag signal?

    Thanks!
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  2. #2
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    chopet!

    From a set of 12 flags, 4 blue,4 red, 2 green, 2 yellow,
    how many types of 12-flag signals are possible?

    Ans: . {12\choose4,4,2,2}\:= \:207,900

    Now what is the answer for 10-flag signals?
    Somewhere, there may be a formula for this problem, but I don't know it . . .

    There are nine possible distributions of colors with ten flags: . (B,\,R,\,G,\,Y) \:=
    . . (4,4,2,0),\:(4,4,1,1),\:(4,4,0,2),\;(4,3,2,1),\:(4  ,3,1,2),\:(4,2,2,2), (3,4,2,1),\:(3,4,1,2),\:(3,3,2,2)

    Now we find the number of each partition and add them.

    . . \begin{array}{ccc}{10\choose4,4,2,0} & = & 3,150 \\ \\<br />
{10\choose4,4,1,1} & = & 6,300 \\ \vdots & & \vdots\end{array}

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