How many ways of creating a PIN code with length of 6 are there?

1,102

Solution 1

The key is the multiplication principle: If a task can be done in $m$ ways and another in $n$ ways, the number of ways we can do both is $mn$.

The idea is that you're choosing a digit from $0$ to $9$ and constructing a six digit PIN. We can start with the case of one digit, then two, then I'll leave it to you to extend to six.

There are only ten one-digit PINs: $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$. Ten digits.

What about two? We could list them out, but let's be smart: this is the same as the concatenation of two one-digit PINs. We have ten choices for the first digit and ten for the second. How many total two-digit PINs are there? By the multiplication prinicple, this is $10 \cdot 10 = 100$. There are a hundred possible 2-digit PINs.

Can you take it from here?

Solution 2

Here is another way to see this

every Pin code of lenth 6 defines a number from 0 to 999,999, that is in total one million numbers.

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Murad
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Updated on December 24, 2022

Comments

  • Murad
    Murad 11 months

    How can i calculate the number of possible PIN codes that use only numbers 0-9 and have length are there? No rules,all numbers can be same or different

  • Murad
    Murad over 6 years
    10 to the power of 6?
  • Sean Roberson
    Sean Roberson over 6 years
    Well done. That's exactly it.
  • Murad
    Murad over 6 years
    wow i'm a genius
  • Yanko
    Yanko over 6 years
    @Murad you are the most brilliant person I have ever met.
  • Murad
    Murad over 6 years
    @yanko My math teacher tells me the same thing