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# help counting

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What fraction of all the 10-digit numbers with distinct digits have the property that no two odd digits are neighboring?

Oct 4, 2021

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Hello Guest,

like 1234567890. For the first digit there are 10 possibilities, for the second digit only 9 possibilities, for the third digit 8 possibilities,... and that makes 10! if you multiply all of them. There are only 2 possibilities that it is odd and even or even and odd, so $$\frac{10!}{2}=1814400 \mbox{ possibilities}$$ .

Straight

Oct 24, 2021