Question

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

Answer 1

There are 362,880 ways to arrange 3 green marbles and 6 red marbles.

Step-by-step explanation:

To find the number of ways 3 green marbles and 6 red marbles can be arranged, we can use the concept of permutations. Permutations give us the number of ways we can arrange a set of objects without repetition.

In this case, we have a total of 9 marbles (3 green + 6 red). We need to find the number of ways we can arrange these 9 marbles. The formula for permutations is:

P(n, r) = n! / (n - r)!

Where 'n' is the total number of objects and 'r' is the number of objects we want to arrange. Plugging in the values, we get:

P(9, 9) = 9! / (9 - 9)! = 9! / 0! = 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

Therefore, there are 362,880 ways to arrange 3 green marbles and 6 red marbles.

Answer 2

`\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

`((G+R)!)/(G!R!)`
`((3+6)!)/(3!\cdot6!)=(9!)/(3!\cdot6!)=(362,880)/((6)\cdot(720))=(362,880)/(4320)=84`

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