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It depends how you define "pair"; and if some of the boys and girls are identical (twins/triplets/etc)

If you mean two people then there are 17 choices for the first (10 boys + 7 girls), 16 (10 boys + 7 girls less the one chosen so far) for the second giving: 17 × 16 = 272 pairs

If you mean a pair containing one boy and one girl, then there are a choice of 10 boys and for each choice a choice of 7 girls, giving: 10 × 7 = 70 pairs.

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Q: How many possible pairs can be chosen from 10 boys and 7 girls?
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