Question

A boy has 6 red , 5 yellow and 4 green marbles. In how many ways can the boy arrange the marbles in a line if:

a)   Marbles of the same color are indistinguishable?

b)  All marbles have different sizes?

Answer 1

A.

`(15!)/(6!5!4!)=(7\cdot8\cdot\ldots\cdot14\cdot15)/(2\cdot3\cdot4\cdot5\cdot2\cdot4\cdot4)=630630`

B.

`15!=1307674368000`