SOLUTION: I have 400 marbles and I want six different colors I also do not want more than two colors to have the same probability. What is the number of each color in each bag and what is th

There are many many ways

20 of the first color
40 of the second color
60 of the third color
80 of the fourth color
100 of the fifth color

That's 20+40+60+80+100 = 300
So use 400-300=100 of the 6th color

Then 

the probability of the 1st color is 20/400 = 1/20
the probability of the 2nd color is 40/400 = 1/10
the probability of the 3rd color is 60/400 = 3/20
the probability of the 4th color is 80/400 = 1/5
the probability of the 5th color is 100/400 = 1/4
the probability of the 6th color is 10/400 = 1/20

-----------------
Another way

1 of the first color
2 of the second color
3 of the third color
4 of the fourth color
5 of the fifth color

That's 1+2+3+4+5 = 15
So use 400-15=385 of the 6th color

Then 

the probability of the 1st color is 1/400
the probability of the 2nd color is 2/400 = 1/200
the probability of the 3rd color is 3/400
the probability of the 4th color is 4/400 = 1/100
the probability of the 5th color is 5/400 = 1/80
the probability of the 6th color is 385/400 = 77/80

Many many ways.  Just make up different numbers for the first 5 colors
then subtract from 400 for the number of the 6th color.  Put them all
over 400 and reduce.

Edwin