Question

if a license plate consists of 2 letters followed by 4 digits, how many different plates could be created having at least one letter or digit repeated?

I know its not 6,760,000

Answer 1

consider the Pr of two letters the same: 1/26

Now consider the Pr of two numbers: 1/10*9/10*8/10
Now the Pr of three numbers the same:
1/10*1/10*9/10
now the Pr of four numbers the same:
1/10*1/10*1/10
now the pr of having two pairs of numbers the same:
1/10*9/10*1/9

Pr(at least one letter or digit repeated:
sum of (two letters, no numbers) + (two letters, two numbers)+(two letters, three numbers)+(two letters, four numbers)+(two letters, two pairs of numbers) + (no letters, two numbers)+(no letters, threenumbers)+(no letters, four numbers)+ (no letters,two pairs of numbers)

I will do the first four probabilities for you:
Pr(twoletters, no numbers)=1/26*9/10*8/10*7/10
Pr(two letters, two numbers)=1/26*1/10*9/10*8/10
Pr(two letters, three numbers)=1/26*1/10*1/10*9/10
See if you can finish.

Answer 2

Your asking for how many combinations and not the probability so ignore the answer above.

First find the number of combinations if all letters and numbers can be repeated
(26*26*10*10*10*10)=6760000

Then find the number of combinations if none were repeated
(26*25*10*9*8*7)=3276000

(value of combinations that can be repeated)-(value of combinations that no letter or number could be repeated) = 6760000-3276000= 3484000

Answer 3

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