How many distinct garlands can be made from flowers of six different colors?

Assuming you have one flower of each color and use all six flowers in your garland-- six factorial.

How many distinct garlands can be made from flowers of six different colors?
wouldn't it be 35 or 36 just a random guess.
Reply:Depends on how many flowers can be in the garland.





Each position can be any one of six colors, so if the number of flowers in the garland is N, then I'd say you could make 6^N garlands, unless it's counted as the same pattern if you turn it around backwards - that is, red-red-blue is the same as blue-red-red. If that's true, then divide by 2.
Reply:How many flowers per garland?





If you assume a garland that holds a maximum of 6 flowers and colors can repeat then there are 7 possibilities for each of 6 positions (one of 6 colors or empty) which would result in (7^6)/6 distinct combinations if there is not a fixed starting point. I'm not sure if that's clear, but you achieve each of the 7^6 pattern 5 additional times by simply moving the starting position until you get back to the original starting position.
Reply:Depends on how many flowers you choose to have, if reversals count, and if you can repeat a color.
Reply:I don't know enough about "garlands". If this is a circle made of six flowers, then the 6! = 720 combinations is wrong, since you can start the circle at any of six places; thus I think the answer is 720/6 = 120.
Reply:Assuming you can only use each color flower either 0 or 1 time, and you need at least 2 flowers for a "garland", and assuming the -order- of the flowers doesn't matter, you can make 50 different garlands. (That's 15 two-flower garlands, 16 three-flower garlands, 15 four-flower garlands, 3 five-flower garlands, and 1 six-flower garland)





Of course, that's a lot of assumptions. You should be more specific in phrasing your question.