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The flag of country A has to contain 3 stripes of the same [#permalink]

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18 Feb 2005, 09:03

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B

C

D

E

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The flag of country A has to contain 3 stripes of the same width, all of which have to be either vertical or horizontal. If the flag of country A must consist of the national colours, which are green, red, yellow, black, and blue, how many differen flags can be created?

My probability sucks but i think for this one it is
5!/(5-3)!=60
but this is different ways of choosing 3 colors, but since the question is how many different combinations are possible on the flag, i think it means that if i pick Black, Yellow, and Red (1 choice) then of this i can have 6 different types of flags right?
So i am confused if order matters or not.
Id still go for 60, it seems like there is more but i am a little lost

see why E?
at most i thought if there are 6 different ways to arrange the colors on the flag (3!)
and it is 60 different ways of choosing the colors shouldnt it be more then??
what was your reasoning?

horizontal: 5 (for the first stripe 5 colors are possible) * 4 (for the second stripe 4 c are possible) * 3 (for the third stripe 3 c are possible) = 60
vertikal: 5*4*3 = 60

can someone suggest an easy, tried-and-tested way to distinguish between permutation and combination problems?
I mistakenly did 5c2 * 2 for this problem, which got me nowhere...

can someone suggest an easy, tried-and-tested way to distinguish between permutation and combination problems? I mistakenly did 5c2 * 2 for this problem, which got me nowhere...

Just ask yourself if you change the orders of two items, does it count as two outcomes for the question.