Question

In how many ways 6 identical red blue and green balls

Answer 1

There are 9 non-green balls; line them all up in a row. Now consider the 8 spaces between the balls, and the 2 spaces at the ends—10 in all. We can put the 4 green balls in any of those spaces (with no more than one in each space). Thus the number of such arrangements is

(104)=210

To this must be considered the multiple ways in which the 3 blue balls can be placed amongst the 9 non-green balls. This is

(93)=84

Thus the total number of possible arrangements is

84 . 210 = 17640