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A team has to design a flag. The team has six blue strips...

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by swerve » Fri Jan 05, 2018 7:28 am
A team has to design a flag. The team has six blue strips of cloth and seven red strips of cloth that they must use as it to make the flag. How many different flags can the team design with the materials at hand?

A. 42
B. 120
C. 720
D. 1,716
E. 5,040

The OA is D.

Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks.
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by ErikaPrepScholar » Fri Jan 05, 2018 7:59 am
Where we have a items of one type, b items of another type, c items of another, etc., we can solve for the number of permutations with the equation:
$$\frac{\left(a+b+c\ ...\right)!}{a!\cdot b!\cdot c!\ ...}$$
We have 13 total stripes. There are 6 of one kind (blue) and 7 of another kind (red). This gives us: $$\frac{(6+7)!}{6!7!}$$ $$\frac{13!}{6!7!}$$ $$\frac{13\cdot12\cdot11\cdot10\cdot9\cdot8}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$$ $$\frac{13\cdot11\cdot9\cdot8}{6}$$ $$1716$$
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