Question

I need to show work for this but I don't know how.

Erik wants to form 4-digit integers using only the digits 1, 2, 3, and 4. He is allowed to
repeat digits. What is the probability that he forms a 4-digit integer where at least one digit
repeats? Express your answer as a common fraction.

Answer 1

there are 10^4 4-digit integers

there are P(10,4) with no repeats

divide P(10,4)/10^4 for the probability of no repeats.

You want 1 minus that probability.

1 - P(10,4)/10^4 = 62/125

so, almost 50%