by kamoda

Question by -M-: How many different colored flags can be made from 10 colors of cloth?
Like its many different colored flags from 10 colors of fabric, with each flag will be on three different stripes?

Best answer:

Answer by Raymond
1st case, not allowed to repeat a color:

first strip can be any of 10 (10 ways)
second strip can be any of the remaining 9
third strip can be any of remaining 8
10*9*8 = 720

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2nd case, adjoining strips must be different
the two outer strips could be of the same color, as long as the centre one is different.

1st strip: any of 10
second (middle) strip: any of remaining 9
third strip: any of the 9 that are different from the middle.

10*9*9 = 810 (of which 720 are already described in 1st case)

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3rd case: no restrictions:

1st strip = any of 10
2nd strip = any of 10
3rd strip = any of 10

10*10*10 = 1,000

of which 10 are solid (one color) = three strips of the same color
and 180 are a double band of one color and a narrow band of another color
(90 with the large band being strips 1 & 2 of the same color; 90 with strips 2 and 3 of the same color)

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orientation?

If you cannot distinguish a reversed flag, then all your totals are to be divided by 2 (except for the solid flag):

If a “red-white-blue” flag is the same as a “blue-white-red” flag, then two combinations give you the same flag.

Add your own answer in the comments!

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