Given that there are 6 boys and 6 girls in a birthday party, the number of different arrangements of first, second, and third is given by:
[tex] ^{12}P_3= \frac{12!}{(12-3)!} \\ \\ = \frac{12!}{9!} = \frac{12\times11\times10\times9!}{9!} \\ \\ =12\times11\times10=1,320[/tex]
