How many ways you can have 5 dancing pairs from 6 boys and 7 girls? Assuming classical dancing pairs (1 boy dancing with 1 girl)
Dancing pairs question, how many ways you can have 5 dancing pairs from 6 boys and 7 girls
combinatoricspermutations
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Best Answer
Pick which five boys are participating in the dance.
From those boys selected, one will be the youngest. Pick which girl dances with the youngest selected boy.
Pick which girl dances with the second youngest selected boy.
Continue in this fashion until all selected boys have a designated dancing partner.
This yields a total of $\binom{6}{5}\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3$