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A bank assigns a 4-digit ID number to each new customer. If each digit is randomly selected from the numbers 0–9, what is the probability that none of the digits repeat?       A. 0.001  B. 0.042  C. 0.021  D. 0.504

Question
   A bank assigns a 4-digit ID number to each new customer. If each digit is randomly selected from the numbers 0–9, what is the probability that none of the digits repeat? 
    
  A. 0.001
  B. 0.042
  C. 0.021
  D. 0.504
check_circleAnswer
Step 1

For any event A, with sample space S, the probability can be found by the formula,

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Step 2

Let A be the even that none of the digits repeat in 4 digit id number.

Each number is selected from 0-9.

There are 10 cases for selecting each digit.

Hence, there are total (10×10×10×10) =10,000 ways for selecting any 4 digit number.

Therefore, n(S)=10,000.

Step 3

Now, for the event A, all four digits are different.

Hence, first digit can be selected in 10 ways, that implies 2nd digit has (10-1) = 9 option to choose, 3rd digit can be chosen in (10-2) = 8 way...

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