1. **State the problem:** We want to find the sample space for the gender of five children in a family. 2. **Understanding sample space:** Each child can be either a boy (B) or a girl (G). 3. **Possible outcomes per child:** Since each child has 2 possible outcomes: boy (B) or girl (G), for 5 children, 4. **Calculate total outcomes:** The total number of possible gender combinations is $$2^5 = 32$$. 5. **List the sample space:** The sample space consists of all 32 sequences of length 5 where each element is either B or G. These include examples like BBBBB, BBBBG, BBBGB, ... GGGGG. 6. **Summary:** Therefore, the sample space S = \{B,G\}^5 with \( |S| = 32 \). **Final answer:** The sample space consists of all 32 possible gender combinations for 5 children.