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# How many 11 -digit positive integers can be written using only the digits 1,2 and 3 and have exactly five 1’s and exactly two 2's as digits?

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How many 11 -digit positive integers can be written using only the digits 1,2 and 3 and have exactly five 1’s and exactly two 2's as digits?

Aug 15, 2022

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We know there must be five 1's, two 2's, and four 3's.

There are $${11! \over 2! \times 5! \times 4!} = \color{brown}\boxed{6930}$$ numbers that work.

Aug 16, 2022