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

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by Anaira Mitch » Sat Oct 21, 2017 4:21 am
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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by [email protected] » Sat Oct 21, 2017 10:45 am
Hi Anaira Mitch,

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: D

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hi

by Scott@TargetTestPrep » Mon Dec 04, 2017 10:34 am
Anaira Mitch 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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