Answer:
1260 ways
Explanation:
The number of ways in which we can arrange n objects where not all are distinct can be calculated as:
[tex]\frac{n!}{n_1!n_2!n_3!}[/tex]Where n is the total number of marbles, and n1, n2, and n3 are the number of marbles of each color. So, there are 9 marbles in total, 3 clear, 4 yellow, and 2 orange.
Then, replacing n by 9, n1 by 3, n2 by 4, and n3 by 2, we get:
[tex]\frac{9!}{3!\cdot4!\cdot2!^{}}=1260[/tex]Therefore, there are 1260 distinct ways to arrange the marbles.
