Combinatorics question

**chopet** · October 9th 2007, 03:15 AM

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!

**Soroban** · October 10th 2007, 01:55 PM

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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