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  • How many different ways can you arrange 15 roses in a row if 5 are red, 7 are yellow, and 3 are orange?Option: 1 360320 n

How many different ways can you arrange 15 roses in a row if 5 are red, 7 are yellow, and 3 are orange?

Option: 1

360320
 


Option: 2

360360
 


Option: 3

360420

 


Option: 4

360430


Answers (1)

best_answer

Given that,

There are 15 roses in a row.

We can arrange the 15 roses in a row is 15! different ways. 

The number of ways to arrange the identical red roses is 5! Ways.

The number of ways to arrange the identical yellow roses is 7! Ways.

The number of ways to arrange the identical orange roses is 3! ways.

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

\begin{aligned} \frac{15 !}{5 ! 7 ! 3 !} & =\frac{15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{5 \times 4 \times 3 \times 2 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 3 \times 2} \\ \frac{15 !}{5 ! 7 ! 3 !} & =15 \times 14 \times 13 \times 12 \times 11 \\ \frac{15 !}{5 ! 7 ! 3 !} & =360360 \end{aligned}

Therefore, the number of ways to arrange the roses is 360360.

 

Posted by

Gautam harsolia

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