Question

14. How many ways can 3 green marbles and 6 red marbles be arranged?

Answer 1

$\begin{gathered} G\to\text{green} \\ R\to\text{red} \end{gathered}$

To find out how many ways we have to order 3 green marbles (G) and 6 red marbles (R) we use the formula the combination

$\frac{(G+R)!}{G!R!}$$\frac{(3+6)!}{3!\cdot6!}=\frac{9!}{3!\cdot6!}=\frac{362,880}{(6)\cdot(720)}=\frac{362,880}{4320}=84$

There are 84 ways to organize the red and the green marbles