# combinations

• May 7th 2010, 05:22 PM
ihavvaquestion
combinations
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 PM
Sudharaka
Quote:

Originally Posted by ihavvaquestion
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???

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= $\frac{6!}{3!\times{3!}}=20$

• May 7th 2010, 05:40 PM
ihavvaquestion
ok i understand the 6! total possible choices, but why DIVIDE by 3!*3!?
• May 7th 2010, 05:58 PM
Sudharaka
Quote:

Originally Posted by ihavvaquestion
ok i understand the 6! total possible choices, but why DIVIDE by 3!*3!?

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

Hope this will clarify.