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counting and probability intermediate

Problem

How many different positive, six-digit integers can be formed using the digits 2, 2, 5, 5, 9 and 9?
Solution
We could go ahead and count these directly, but instead we could count in general and then correct for overcounting. That is, if we had 6 distinct digits, there would be orderings. However, we must divide by 2! once for the repetition of the digit 2, 2! for the repetition of the digit 5, and again 2! for the repetition of the digit 9 (this should make sense because if the repeated digits were different then we could rearrange them in 2! ways). So, our answer is .
Final answer
90