Five red balls, two white balls and three blue balls are ordered randomly on a table. Suppose balls of the same color can not be distinguished

from each other (i.e. the ordering of balls with the same color does not

matter). What is the probability that balls with the same color are ordered

together (i.e. there are no blue or white balls between red balls, no red or

blue balls between white balls, and no red or white balls between blue balls)

?