SOLUTION: How many ways are there of choosing 6 colors, without replacement, from distinct 10 colors, if the order if the choices is not relevant? the order of the choices is relevant?

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Question 820286: How many ways are there of choosing 6 colors, without replacement, from distinct 10 colors, if the order if the choices is not relevant? the order of the choices is relevant?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
When the order is relevant...
When picking the first color there are 10 choices. When picking the second color there are 9 choices (since we can't use the color already chosen). When picking the third color there are 8 choices (since we can't use the two colors already chosen), etc. Altogether there are:
10*9*8*7*6*5 = 151200 choices.

When the order is not relevant...
We start with 10*9*8*7*6*5 and then "remove" the "duplicates". This is done by dividing by 1*2*3*4*5*6:
%2810%2A9%2A8%2A7%2A6%2A5%29%2F%281%2A2%2A3%2A4%2A5%2A6%29+=+210 choices.

Note that there are 6 factors in the numerator and denominator. This is how many choices we made. And note that the factors in the numerator start from 10, the number of colors we had to choose from, and went down from there.

So if we had 14 colors and were choosing 8 then there would be
14*13*12*11*10*9*8*7 possible arrangements when the order is relevant and
%2814%2A13%2A12%2A11%2A10%2A9%2A8%2A7%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29 possible arrangements when the order is not relevant.