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

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If an employee ID code must consist of 3 non-repeating digit [#permalink]

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27 Aug 2011, 21:31
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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

source Jamboree
[Reveal] Spoiler: OA

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Last edited by abhimahna on 02 Jan 2017, 20:56, edited 2 times in total.

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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink]

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28 Aug 2011, 02:35
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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]

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29 Nov 2017, 21:05
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Expert's post
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.

[Reveal] Spoiler:
D

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Re: If an employee ID code must consist of 3 non-repeating digit [#permalink]

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04 Dec 2017, 10:34
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.

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Re: If an employee ID code must consist of 3 non-repeating digit   [#permalink] 04 Dec 2017, 10:34
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