Question

In how many ways can 3 boy and 3 girl students be seated in a row each student is labeled either b (boy) or g (girl)? Option 1: 168 Option 2: 20160 Option 3: 720 Option 4: 5040

Answer 1

The answer is Option 3: 720.

Explanation:

he number of ways to arrange 3 boys and 3 girls in a row is given by the permutation formula:

P(6,6) = 6!/(6-6)! = 6!

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where P(n,r) denotes the number of permutations of n objects taken r at a time. Since there are no restrictions on the arrangement of boys and girls, we can simply multiply the total number of permutations by the number of ways to arrange the boys and girls separately.

The number of ways to arrange 3 boys in a row is given by:

P(3,3) = 3!/(3-3)! = 3!

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Similarly, the number of ways to arrange 3 girls in a row is also given by:

P(3,3) = 3!/(3-3)! = 3!

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Therefore, the total number of ways to arrange 3 boys and 3 girls in a row is:

P(6,6) = P(3,3) * P(3,3) * 6! = 6! = 720

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Therefore, the answer is Option 3: 720.