SOLUTION: A newly married couple is planning to have 5 children. How many possible gender combinations are there ?

Question 1114270: A newly married couple is planning to have 5 children. How many possible gender combinations are there ?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
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There are = 32 possible gender combinations.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The problem is not clearly defined.

One possible interpretation is like that by tutor ikleyn. Each child can be either a boy or girl (2 choices), so with 5 children the number of different sequences of 5 children is 2^5 = 32.

However, the statement of the problem asks for the possible number of gender combinations; in formal mathematics that means we are not interested in the order of the boys and girls in the family.

With that interpretation of the problem, there are only 6 possible combinations:
0 boys, 5 girls
1 boy, 4 girls
2 boys, 3 girls
3 boys, 2 girls
4 boys, 1 girl
5 boys, 0 girls

We can't be sure of which question you were really asking....
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