Distinct ages of three children between 7 and 15

Question

Three siblings all have different ages (whole years). The youngest is $7$ or older and the eldest is $15$ or younger. How many possible sets of ages are there?

Short answer

$84$ . Any $3$ distinct values from $\{7,8,\dots,15\}$ (nine values) give a valid set, and the order is determined by age, so the count is $\binom93=84$ .

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Lessons behind this question

Counting and Combinatorics

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