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If an employee ID code must consist of 3 non-repeating digit

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Marcab
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If an employee ID code must consist of 3 non-repeating digit [#permalink] New post   Updated on: 02 Jan 2017, 21:56
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If an employee ID code must consist of 3 non-repeating digits and each digit is in the code must be a prime number, how many ID codes can be generated?
(a) 4
(b) 10
(c) 22
(d) 24
(e) 26

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D

Originally posted by Marcab on 27 Aug 2011, 22:31.
Last edited by abhimahna on 02 Jan 2017, 21:56, edited 2 times in total.
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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink] New post   29 Nov 2017, 22:05
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Hi All,

We're told that an ID code must consist of 3 non-repeating digits and each digit is in the code must be a PRIME number. We're asked for the number of ID codes that can be generated.

Since we're limited to just PRIME numbers/digits, we can only use the numbers 2, 3, 5 and 7. With a 3-digit code that uses NON-REPEATING digits, we can calculate the total number of possibilities by working through one digit at a time:

For the 1st digit, there are 4 options. Once we choose one....
For the 2nd digit, there are 3 options. Once we choose one...
For the 3rd digit, there are 2 options...

(4)(3)(2) = 24 possible ID codes.

Final Answer:
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D


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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink] New post   28 Aug 2011, 03:35
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siddharthasingh wrote:
If an employee ID code must consist of 3 non-repeating digits and each digit is in the code must be a prime number, how many ID codes can be generated?

sorry no options were given


source Jamboree


There are 4 prime number digits
2,3,5,7

We need to select 3 out of 4 and rearrange them in 3! ways.

So,
\(C^{4}_{3}*3!\)

OR, using permutation

\(P^{4}_{3}\)

Ans: 24.

***************************************

If the digits could be repeated:

\(4^3\)
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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink] New post   04 Dec 2017, 11:34
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Marcab wrote:
If an employee ID code must consist of 3 non-repeating digits and each digit is in the code must be a prime number, how many ID codes can be generated?
(a) 4
(b) 10
(c) 22
(d) 24
(e) 26


The possible single-digit primes are 2, 3, 5, and 7.

Since the order of the digits in the code is important, we use permutations. Thus, the number of ways in which 3 non-repeating prime digits can selected is 4P3 = 4 x 3 x 2 = 24.

Answer: D
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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink] New post   28 Jun 2020, 01:39
What the answer would be if repetition is allowed..meaning you could have 222, 333, 223..etc...
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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink] New post   28 Jun 2020, 15:20
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sony1000 wrote:
What the answer would be if repetition is allowed..meaning you could have 222, 333, 223..etc...


Hi sony1000,

IF we were allowed to have repeating digits, then the number of options for each digit would be the SAME. Thus, the total number of codes would be (4)(4)(4) = 64.

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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink] New post   02 Nov 2022, 10:13
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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink]
02 Nov 2022, 10:13
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