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How many four-digit, positive integers are there where each digit is a prime number?
 

Ty to whoever answers :)

 May 24, 2024
 #1
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It should be 24 aka 4! since there are that many arrangements of four digit postivies intigers.  If you still don't understand let me know :)

 

- Chad

 May 24, 2024
 #2
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Here's what I found....

 

The prime digits wil be  2,3,5,7

 

Cases :

 

Case 1 :  all the digits are the same  =  4  ways to do this 

 

Case 2 :  three of the digits are the same

      4 ways to select the same three digits  

      Then, select any one of the three remaining digits  to occupy any of  four places

      4  * 3 * 4  =  48

  

Case 3:  two of the digts are the same

     4 ways two select the same two digits 

     Choose any two of the remaining  three primes 3C2 = 3  to occupy any two of four positions 4C2 = 6

      4 * 3 * 6  =  72

 

Case 4 :  all the digits are different  =  4!  = 24

 

Total  =   4 + 48  + 72 + 24  =   148 

 

cool cool cool

 May 24, 2024
edited by CPhill  May 24, 2024

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