Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and the Binomial Theorem - 10.2 Exercises - Quiz for Lessons 10.1-10.2 - Page 697: 16

$750$

We know that if we want to select $r$ objects out of $n$ disregarding the order, we can do this in $_nC_r=\frac{n!}{r!(n-r)!}$ ways. Here we have $n_1=5,r_1=1$ for the cheese, $n_2=10,r_2=1$ for the vegetable, and $n_3=6,r_3=2$ for the meats: $_{5}C_1\cdot_{10}C_1\cdot_{6}C_2=\frac{5!}{4!1!}\frac{10!}{9!1!}\frac{6!}{4!2!}=5\cdot10\cdot15=750$