Problem 13 · 2011 Math Kangaroo
Hard
Counting & Probability
careful-counting
48 children are going on a ski trip. Six of them go with exactly one sibling, nine go with exactly two siblings, and four go with exactly three siblings. The remaining children go without any siblings. How many families are going on the trip?
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Answer: D — 36
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Hint 1 of 2
'Exactly one sibling' means a family of two; 'two siblings' a family of three, and so on.
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Hint 2 of 2
Turn each group of children into a count of families, then add the only-children.
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Approach: convert children-with-k-siblings into families
- 6 children with one sibling → 3 families of 2; 9 with two siblings → 3 families of 3; 4 with three siblings → 1 family of 4.
- Children with siblings: 6+9+4 = 19, leaving 48−19 = 29 only-children → 29 families.
- Total families = 3+3+1+29 = 36.
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