Chapter 11 - Counting Methods and Probability Theory - Chapter Summary, Review, and Test - Review Exercises - Page 758: 27

$55440$

We know that if we want to select $r$ objects out of $n$ disregarding the order, we can do this in $_nC_r=\frac{n!}{(n-r)!r!}$ ways. Hence here the number of possibilities: $_{12}P_5\cdot_{8}P_4=\frac{12!}{(12-5)!5!}\frac{8!}{(8-4)!4!}=55440$