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How many six-digit positive integers can be written using only the digits 1,2  and 3 and have exactly two 1's, two 2's, and two 3's as digits?

I have no idea how to start with this question

 Aug 12, 2022
 #1
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1, 1, 2, 2, 3, 3 ==6! / [2!2!2!] ==720 / 8 ==90 - permutations

 

[(1, 1, 2, 2, 3, 3), (1, 1, 2, 3, 2, 3), (1, 1, 2, 3, 3, 2), (1, 1, 3, 2, 2, 3), (1, 1, 3, 2, 3, 2), (1, 1, 3, 3, 2, 2), (1, 2, 1, 2, 3, 3), (1, 2, 1, 3, 2, 3), (1, 2, 1, 3, 3, 2), (1, 2, 2, 1, 3, 3), (1, 2, 2, 3, 1, 3), (1, 2, 2, 3, 3, 1), (1, 2, 3, 1, 2, 3), (1, 2, 3, 1, 3, 2), (1, 2, 3, 2, 1, 3), (1, 2, 3, 2, 3, 1), (1, 2, 3, 3, 1, 2), (1, 2, 3, 3, 2, 1), (1, 3, 1, 2, 2, 3), (1, 3, 1, 2, 3, 2), (1, 3, 1, 3, 2, 2), (1, 3, 2, 1, 2, 3), (1, 3, 2, 1, 3, 2), (1, 3, 2, 2, 1, 3), (1, 3, 2, 2, 3, 1), (1, 3, 2, 3, 1, 2), (1, 3, 2, 3, 2, 1), (1, 3, 3, 1, 2, 2), (1, 3, 3, 2, 1, 2), (1, 3, 3, 2, 2, 1), (2, 1, 1, 2, 3, 3), (2, 1, 1, 3, 2, 3), (2, 1, 1, 3, 3, 2), (2, 1, 2, 1, 3, 3), (2, 1, 2, 3, 1, 3), (2, 1, 2, 3, 3, 1), (2, 1, 3, 1, 2, 3), (2, 1, 3, 1, 3, 2), (2, 1, 3, 2, 1, 3), (2, 1, 3, 2, 3, 1), (2, 1, 3, 3, 1, 2), (2, 1, 3, 3, 2, 1), (2, 2, 1, 1, 3, 3), (2, 2, 1, 3, 1, 3), (2, 2, 1, 3, 3, 1), (2, 2, 3, 1, 1, 3), (2, 2, 3, 1, 3, 1), (2, 2, 3, 3, 1, 1), (2, 3, 1, 1, 2, 3), (2, 3, 1, 1, 3, 2), (2, 3, 1, 2, 1, 3), (2, 3, 1, 2, 3, 1), (2, 3, 1, 3, 1, 2), (2, 3, 1, 3, 2, 1), (2, 3, 2, 1, 1, 3), (2, 3, 2, 1, 3, 1), (2, 3, 2, 3, 1, 1), (2, 3, 3, 1, 1, 2), (2, 3, 3, 1, 2, 1), (2, 3, 3, 2, 1, 1), (3, 1, 1, 2, 2, 3), (3, 1, 1, 2, 3, 2), (3, 1, 1, 3, 2, 2), (3, 1, 2, 1, 2, 3), (3, 1, 2, 1, 3, 2), (3, 1, 2, 2, 1, 3), (3, 1, 2, 2, 3, 1), (3, 1, 2, 3, 1, 2), (3, 1, 2, 3, 2, 1), (3, 1, 3, 1, 2, 2), (3, 1, 3, 2, 1, 2), (3, 1, 3, 2, 2, 1), (3, 2, 1, 1, 2, 3), (3, 2, 1, 1, 3, 2), (3, 2, 1, 2, 1, 3), (3, 2, 1, 2, 3, 1), (3, 2, 1, 3, 1, 2), (3, 2, 1, 3, 2, 1), (3, 2, 2, 1, 1, 3), (3, 2, 2, 1, 3, 1), (3, 2, 2, 3, 1, 1), (3, 2, 3, 1, 1, 2), (3, 2, 3, 1, 2, 1), (3, 2, 3, 2, 1, 1), (3, 3, 1, 1, 2, 2), (3, 3, 1, 2, 1, 2), (3, 3, 1, 2, 2, 1), (3, 3, 2, 1, 1, 2), (3, 3, 2, 1, 2, 1), (3, 3, 2, 2, 1, 1)] >Total distinct permutations = 90

 Aug 12, 2022

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