Question 1114270
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The problem is not clearly defined.<br>
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.<br>
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.<br>
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<br>
We can't be sure of which question you were really asking....