# 1. How many 4-digit codes can be made if no digit can repeat? 2. How many ways can 5 bikes be displayed in a store window from a group of 12?

##### 1 Answer

Dec 18, 2016

#=5040# , 2.#=792#

#### Explanation:

First problem: 4-digit codes where no digit repeats:

The first digit can be anything from 0-9, so we have 10 choices.

The second digit can by anything except the first digit, so we have 9 choices

The third digit we have 8 choices

The fourth digit we have 7 choices:

Second problem: There are 12 bikes to choose from and we want to display 5. Since choosing bikes 1, 2, 3, 4, 5 is the same as choosing bikes 5, 4, 3, 2, 1 we have a combinations problem.

and now let's evaluate it: