Question

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

Answer 1

The awnser is 1,814,400

Explanation:

I took the test

Answer 2

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=(10!)/(8!(10-8)!)=(10!)/(8! * 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! * (10!)/(8! * 2!)=(10!)/(2!)=(2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10)/(2)=1814400`

He can arrange 8 jars on the spice rack in c. 1,814,400 ways.