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.

$\dfrac{15!}{6!5!4!}=\dfrac{7\cdot8\cdot\ldots\cdot14\cdot15}{2\cdot3\cdot4\cdot5\cdot2\cdot4\cdot4}=630630$

B.

$15!=1307674368000$