Unlock the four-digit lock

Probability Level 1

Unfortunately you can’t remember the code for your lock, which accepts combinations from 0000 to 9999. You only know that you didn’t use any digit more than once. How many different ways do you have to try?

The answer is 5040.

4 solutions

Farhan Tanvir Mridul
Apr 6, 2014

There are 10 digits (0, 1, …, 9) and each one appears at most once. The number of orderings of these digits is 10P4 = 5040.

what is the p Stands For ?

Demigod Sayan - 7 years, 2 months ago

permutation...check out your scientific calculator nPr button

Farhan Tanvir Mridul - 7 years, 2 months ago

For the first code you may use any of the 10 digits. So we may try any of the 10 digits in first case. So then in the second case we are left with 9 possible digits as we already have used 1 digit and that digit cannot be repeated. Then again in the third case we may use any of the 8 left digits as we have already used 2 digits. And in the last case we may try 7 digits.

So number of possible ways = 10x9x8x7=5040

Tanjim Faruk - 7 years, 1 month ago

A 4-digit number cannot start with a '0'. So we cannot use 0 at first place. So, we are left with 9 possibilities for the first place. And 9 for the second since 0 can be present .So Ideally, isn't it 9 * 9 * 8 * 7?

hari haran - 6 years, 11 months ago

"the code for your lock, which accepts combinations from 0000 to 9999."

Saya Suka - 3 months, 1 week ago