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  • How many different ways are there to arrange 10 marbles in a row if 3 of them are red, 3 are blue, and 4 are green?Option: 1 <img alt="1200

How many different ways are there to arrange 10 marbles in a row if 3 of them are red, 3 are blue, and 4 are green?

Option: 1

1200


Option: 2

2100


Option: 3

4200


Option: 4

3500


Answers (1)

best_answer

Given that,

There are 10 marbles in a row.

We can arrange the 10 marbles in a row in 10! different ways. 

The number of ways to arrange the identical red marbles is 3! Ways.

The number of ways to arrange the identical blue marbles is 3! Ways.

The number of ways to arrange the identical green marbles is 4! ways.

Thus, the total number of possible arrangements is given by,

\begin{aligned} & \frac{10 !}{3 ! 3 ! 4 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{3 \times 2 \times 3 \times 2 \times 4 \times 3 \times 2} \\ & \frac{10 !}{3 ! 3 ! 4 !}=10 \times 3 \times 4 \times 7 \times 5 \\ & \frac{10 !}{3 ! 3 ! 4 !}=4200 \end{aligned}

Therefore, the number of ways to arrange the marbles is 4200.

Posted by

Rakesh

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