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  • In a classroom, there are 5 boys and 7 girls. How many different ways are there to arrange the students in a row with the boys sitting in the odd-numbered seats?<div class='qna-opti

In a classroom, there are 5 boys and 7 girls. How many different ways are there to arrange the students in a row with the boys sitting in the odd-numbered seats?

Option: 1

604800


Option: 2

513400


Option: 3

783200


Option: 4

453300


Answers (1)

best_answer

To determine the number of different ways to arrange the students in a row with the 5 boys sitting in the odd-numbered seats, we can consider the following:

Since the boys must sit in the odd-numbered seats, we can treat them as a single entity and arrange them in the odd-numbered seats first. Similarly, we can treat the girls as a single entity and arrange them in even-numbered seats.

The number of ways to arrange the 5 boys in the odd-numbered seats can be calculated as the factorial of the number of boys (5! in this case).

Similarly, the number of ways to arrange the 7 girls in the even-numbered seats can be calculated as the factorial of the number of girls (7! in this case).

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

\begin{aligned} & 5 ! \times 7 !=120 \times 5040 \\ & 5 ! \times 7 !=604800 \end{aligned}

Hence, there are 604,800 different ways to arrange the students in a row with the 5 boys sitting in the odd-numbered seats.


 

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vinayak

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