What is the probability that a random r-digit number (r 3)

Chapter , Problem 30

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QUESTION:

What is the probability that a random r-digit number (r 3) contains at least one 0, at least one 1, and at least one 2?

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QUESTION:

What is the probability that a random r-digit number (r 3) contains at least one 0, at least one 1, and at least one 2?

ANSWER:

Step 1 of 3

Let be the event that the random digit number contains at least one , be the event that the random digit number contains at least one and be the event that the random digit number contains at least one .

Then,

                                     

Now, we will calculate .

By the inclusion exclusion principle,

                                     

 

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