A 4 digit phone lock using the digits 4, 2, 3 and 0

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Question from Ragu, a student:

I would like to know formula for searching a combination of 4 digit. eg.

I knew my Phone Lock combination is my car plate number 4230. But
this time, i used another way around instead of 4230.

But I am sure, there is only this 4 digits only. 4 & 2 & 3 & 0.

Appreciate if you could help on this.

Thanks
Ragu

Hi,

You have the four digits 4, 2, 3 and 0 and you want to arrange them in all possible orders. These are called the permutations of the digits 4, 2, 3 and 0. There are not very many possibilities so you can write them down.

There are four possibilities for the first digit, 4, 2, 3 and 0. No matter which digit you chose for the first digit there are three remaining digits for the second digit. Thus your choices so far are

42
43
40

24
23
20

34
32
30

04
02
03

There are $4 \times 3 = 12$ of them.

For each of the twelve, two digit numbers above how many choices are there for the third digit. Write them all down. How many are there? What about the last digit?

I hope this helps,
Penny

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