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How many different ways are there to arrange 12 water bottles on a shelf if 4 of them are yellow, 4 are red, and 4 are orange?

 

Option: 1

34650


Option: 2

24550


Option: 3

44750

 


Option: 4

53450


Answers (1)

best_answer

There are 12 water bottles on a shelf.

We can arrange the 12 water bottles on a shelf in 12! different ways. 

The number of ways to arrange the yellow water bottles is 4! Ways.

The number of ways to arrange the red water bottles is 4! Ways.

The number of ways to arrange the orange water bottles is 4! ways.

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

\begin{aligned} &\begin{aligned} \frac{12 !}{4 ! 4 ! 4 !} & =\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{4 \times 3 \times 2 \times 4 \times 3 \times 2 \times 4 \times 3 \times 2} \\ \frac{12 !}{4 ! 4 ! 4 !} & =11 \times 10 \times 9 \times 7 \times 5 \end{aligned}\\ &\frac{12 !}{4 ! 4 ! 4 !}=34650 \end{aligned}

Therefore, the number of ways to arrange the water bottles on a shelf is 34650.

Posted by

Sanket Gandhi

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