Choose the one alternative that best completes the statement or answers the question.
-If a couple has six boys and six girls, how many gender sequences are possible?
A)924
B)12
C)8
D)16

Question

Quizplus · Accepted Answer

There are 12 children, so the number of gender sequences can be calculated using the formula for permutations: P(12,12) = 12!/(12-12)! = 12! = 479001600. However, since we only need to consider the gender sequences, we need to divide by the number of ways the boys and girls can be ordered within their own groups, which is given by 6! and 6!, respectively. Therefore, the total number of possible gender sequences is 12!/(6!6!) = 924. The number of gender sequences can be found by calculating the number of ways to arrange 12 items (6 boys and 6 girls) in a row, which is 12!. However, we must divide by the number of ways to arrange the identical items, which is 6! for the boys and 6! for the girls. Therefore, the total number of gender sequences is 12!/6!6! = 924.

Choose the One Alternative That Best Completes the Statement or Answers