there are 5 red marbles, 3 blue and 4 black of different sizes. In how many ways they can be put in a row so that the marbles of same color are always together?

Question

there are 5 red marbles, 3 blue and 4 black of different sizes. In how many ways they can be put in a row so that the marbles of same color are always together?

Answer 1

There are 3! ways to arrange the three colors.

Within each color, there are 5!,3!,4! ways to arrange the different marbles.

So, there are 3!5!3!4! = 103680 ways to arrange the marbles as specified.