SOLUTION: four random digits are drawn (repetition are allowed). Among the four digits, in how many ways can two or more repetitions occur?

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Question 849420: four random digits are drawn (repetition are allowed). Among the four digits, in how many ways can two or more repetitions occur?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
I will assume that 2922 and 7777 have more than one repetition,
even though there is only one digit that is repeated.
However, if these are to be considered to have only one repetition, 
then tell us that in the thank-you note, and we'll get back to you,
and solve it that way.

The total number of ways 4 digits can be drawn is

10×10×10×10 = 104 = 10000

We will calculate the number of those that have

1. No repetitions (such as 0927)

That's 10×9×8×7 = 5040 

2. exactly 1 repetition. (such as 4575)

Choose the digit to repeat any of 10 ways
Choose the 2 positions to place that repeating digit C(4,2) = 6 ways
Choose a digit to place in the leftmost unfilled position 9 ways.
Choose a digit to place in the rightmost unfilled position 8 ways.

That's 10×6×9×8 = 4320

So that's 5040+4320 or 9360 to subtract from 10000

10000-9360 = 640 

Answer: 640

Edwin