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  • A collection of 12 postage stamps includes 3 American stamps, 4 European stamps, and 5 Asian stamps. In how many ways can the stamps be arranged in a row?  <div class='qna-option

A collection of 12 postage stamps includes 3 American stamps, 4 European stamps, and 5 Asian stamps. In how many ways can the stamps be arranged in a row?

 

Option: 1

27720


Option: 2

25430


Option: 3

21054


Option: 4

22315


Answers (1)

best_answer

Given that,

There are 12 postage stamps including 3 American stamps, 4 European stamps, and 5 Asian stamps.

We can arrange the 12 postage stamps in a row in 12! different ways. 

The number of ways to arrange the 3 American stamps is 3! Ways.

The number of ways to arrange the 4 European stamps is 3! Ways.

The number of ways to arrange the 5 Asian stamps is 4! ways.

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

\begin{aligned} & \frac{12 !}{3 ! 4 ! 5 !}=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{3 \times 2 \times 4 \times 3 \times 2 \times 5 \times 4 \times 3 \times 2} \\ & \frac{12 !}{3 ! 4 ! 5 !}=11 \times 5 \times 9 \times 8 \times 7 \\ & \frac{12 !}{3 ! 4 ! 5 !}=27720 \end{aligned}

Therefore, the number of ways to arrange the stamps is 27720.

 

 

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