Answered

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In how many ways can 6 boys and 6 girls be seated at a round table so that boys and girls are to sit alternately?

Sagot :

Zjuidn

It is much easier to solve this if we think of it as arranging the 6 boys and 6 girls in a row first.

If the boys and girls are to sit alternately, there are two possible arrangements: BGBGBGBGBGBG or GBGBGBGBGBGB.

There are 2*6!*6! = 1,036,800 ways to arrange them if they are in a row.

But since we are arranging them at a round table, we should remove the cyclic permutations. We only count the circular permutations. We will divide the linear permutations by the total number of objects 12 to get the answer 1,036,800/12 = 86,400.

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