He has 10 spice jars, but the spice rack only holds 8 spice jars.
Calculate in how many ways he can choose 8 spice jars from 10 spice jars using combination:
\(_{10} C _8=\frac{10!}{8!(10-8)!}=\frac{10!}{8! \times 2!}\)
Each combination of 8 spice jars that he chooses he can arrange in 8! ways.
He can choose 8 spice jars in (10!)/(8!×2!) ways and arrange each combination in 8! ways.
Using the rule of product:
\(8! \times \frac{10!}{8! \times 2!}=\frac{10!}{2!}=\frac{2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10}{2}=1814400\)
He can arrange 8 jars on the spice rack in c. 1,814,400 ways.
