A chef has 10 spice jars, but his new spice rack only holds 8 spice jars. How many ways can he arrange 8 jars on the spice rack?
a. 45
b. 80
c. 1,814,400
d. 3,628,800
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: [tex]_{10} C _8=\frac{10!}{8!(10-8)!}=\frac{10!}{8! \times 2!}[/tex]
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: [tex]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[/tex]
He can arrange 8 jars on the spice rack in c. 1,814,400 ways.
