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4 boys and 4 girls are to be seated in a row. The number of ways in which this can be done, if the boys and girls sit alternately, is

  • a)
    4! × 4!

  • b)
    P(8,8)

  • c)
    2 ×4! × 4!

  • d)
    none of these

Correct answer is option 'C'. Can you explain this answer?
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To solve this problem, we can consider the positions of the boys and girls separately.

First, let's consider the positions of the boys. There are 4 boys, so we have 4 options for the first position, 3 options for the second position, 2 options for the third position, and 1 option for the fourth position. This gives us a total of 4! = 24 ways to arrange the boys.

Next, let's consider the positions of the girls. Similarly, there are 4 girls, so we have 4 options for the first position, 3 options for the second position, 2 options for the third position, and 1 option for the fourth position. This also gives us a total of 4! = 24 ways to arrange the girls.

Since the boys and girls must sit alternately, the total number of ways to arrange the boys and girls is the product of the number of ways to arrange the boys and the number of ways to arrange the girls. Therefore, the total number of ways to seat the boys and girls is 24 * 24 = 576.

So the correct answer is 576, not 4!.
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4 boys and 4 girls are to be seated in a row. The number of ways in which this can be done, if the boys and girls sit alternately, isa)4!×4!b)P(8,8)c)2×4!×4!d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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