# How many ways one can put prime numbers to form 3 digit NIP?

## Homework Statement

as listed above the question is how many and which three digit NIP can be formed whit the use of prime numbers[/B]

## Homework Equations

nothing currently trying to understand[/B]

## The Attempt at a Solution

well i have found at least 168 primer numbers below 1000 i mean in the range of three digit,
and grouped in three groups:
numbers of 1 digit "4"
numbers of two digit "21"
numbers of three digit ""143"
as far i know this is a permutation because order matters so 717 is diferent of 177 and 771 so
i am thinking of like a billion of ways to put those numbers to form a NIP, my question is this is even doable?
how can i start to mix this to make to the final count of how many ways one can put all those numbers to form the NIPS
***** update: i think for the three digit numbers there is a rule of 3! on each one so making 6 ways to put that number so if i multiply that for 143 this gives me 858 ways in total but i dont know if this is correct, and its just for the three digit numbers
**** second update:
i permuted every 1 digit number whit every 2 digit number
11 and 2,3,5,7 ok then 112, 211,121. so 3!=6 then 6*4 the 4 represent the 1 digit numbers
24 is the total acoding to this so 24*21 21 represents the total 2 digit numbers, this gives to me
504 but previously i ve calculated the permutation of 3 digit numbers so using the prefix "and"
504*858=432432
i dont know if i am right can you help me?

Last edited:

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WWGD
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What is an NIP?

i guees the number for the bank and things like that only uses numbers and not letters

WWGD
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Do you mean PIN, personal identification number?

yes but in my homework says NIP

WWGD
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Can you find out how it is defined?

is in spanish "numero identificacion personal" check my lastest update

WWGD
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Ok, did not expect Spanish with that username. Seems you have the option for 3, of 4P3= ##\frac {4!}{1!}=4!=24 ## with just one digit. Then you can have combinations of a 1-digit prime in the 1st, 2nd or 3rd spot and a two-digit prime in the remaining two spots ( if you allow this; maybe you just allow a 1-digit prime in spot 1 and a 2-digit prime afterwards or a 1-digit prime in spot 3 and a two-digit prime in the first two spots, and then consider all the 3-digit primes.

so my analisis in the update its all right? or have some flaws

my new doubt is if do i need to multiply the results?
i mean the 24 forms of the 1 digit numbers, the 504 form for the two digit numbers and 1 digit number and the 858 form of the three digit numbers?
24*504*858=?

haruspex
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can be formed whit the use of prime numbers
This is too vague.
It could mean just using prime digits, or concatenating 1-, 2- and 3-digit primes.
I'm pretty sure it does not mean more convoluted uses like this:
i think for the three digit numbers there is a rule of 3! on each one so making 6 ways to put that number
If you allow that sort of thing then you can almost surely make every 3-digit number not ending in zero. Your multiply by 6 rule will in itself count duplicates, e.g.133 would be counted twice.

WWGD
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2019 Award
This is too vague.
It could mean just using prime digits, or concatenating 1-, 2- and 3-digit primes.
I'm pretty sure it does not mean more convoluted uses like this:

If you allow that sort of thing then you can almost surely make every 3-digit number not ending in zero. Your multiply by 6 rule will in itself count duplicates, e.g.133 would be counted twice.
Yes, this is where I sort of got stuck. It seems to need a version of multinomial coefficients, you know, the Mississippi thing..

WWGD
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my new doubt is if do i need to multiply the results?
i mean the 24 forms of the 1 digit numbers, the 504 form for the two digit numbers and 1 digit number and the 858 form of the three digit numbers?
24*504*858=?
Look up multinomial coefficients. These help you answer, e.g., the number of permutations of a word like Mississippi ( with many repeats ) as ## \frac {11!}{2!4!4!} ##; 4 repeats for s, for for i and 4 for p.

yes i also think this is too vague, i will keep working on this and keep you updated.

haruspex
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yes i also think this is too vague, i will keep working on this and keep you updated.
My best guess is that the question just means using prime digits.

1 digit prime numbers?

haruspex
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1 digit prime numbers?
Yes. If it does not mean that, my next guess is using 3-digit prime numbers and concatenating 1-, and 2-digit prime numbers in either order, but certainly nothing more complicated than that.

Yes, I didn't tough about the repeating numbers in the 3 digit, ultimately I will ask my professor tomorrow and update, I only hope this don't come in the test

haruspex