How many different signals can be sent up on a flag pole if each signal requires three yellow and three blue flags and the flags are identical except for color?

would this just be 6C3 times 6C3???

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- May 7th 2010, 05:22 PMihavvaquestioncombinations
How many different signals can be sent up on a flag pole if each signal requires three yellow and three blue flags and the flags are identical except for color?

would this just be 6C3 times 6C3??? - May 7th 2010, 05:34 PMSudharaka
Dear ihaveaquestion,

If the six flags are identical we could send send 6! different signals.

But since there are 3 similar flags of yellow and 3 similar flags of blue,

No. of different signals that could be sent= $\displaystyle \frac{6!}{3!\times{3!}}=20$

Hope this will help you. - May 7th 2010, 05:40 PMihavvaquestion
ok i understand the 6! total possible choices, but why DIVIDE by 3!*3!?

- May 7th 2010, 05:58 PMSudharaka
Dear ihavvaquestion,

Since the total possible choices (6!) contains repeated arrangements,

Take the number of**different**arrangements as N.

Therefore, since there are three yellow flags and three blue flags interchanging them will will give you the total possible choices.

Hence, $\displaystyle N\times{3!}\times{3!}=6!\Rightarrow{N=\frac{6!}{3! \times{3!}}}$

Hope this will clarify.