Question

Keyless door entries require you to input your 6 digit passcode in the correct order. How many different 6 digit passcodes can be created from 10 digits, if all of the digits must be distinct?

Give your answer in simplest form.

Provide your answer below:

Answer 1

151200

Explanation:

We want to know how many permutations of 6 digits can be chosen from 10 different digits, so we use the formula:

nPr=n!(n−r)!

Here, r=6 and n=10, so we have:

10P6=10!(10−6)!=10!4!=10⋅9⋅8⋅7⋅6⋅5⋅4!4!=151,200