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(C) The last digit of a product of $n$ integers is $2, 4, 6,$ or $8$ if the product is even but not a multiple of $5$. An integer ends in $0, 1, 2, 3,

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$\frac{4^n - 2^n}{5^n}$

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(C) The last digit of a product of $n$ integers is $2, 4, 6,$ or $8$ if the product is even but not a multiple of $5$. An integer ends in $0, 1, 2, 3, 4, 5, 6, 7, 8,$ or $9$. The probability that an integer does not end in $0$ or $5$ is $\frac{8}{10} = \frac{4}{5}$. The probability that the product of $n$ integers does not end in $0$ or $5$ is $(\frac{4}{5})^n$. Among the digits ${1, 2, 3, 4, 6, 7, 8, 9}$,the product ends in $2, 4, 6,$ or $8$ if it is even. The product is odd if all $n$ integers end in ${1, 3, 7, 9}$. The probability of an integer ending in ${1, 3, 7, 9}$ is $\frac{4}{10} = \frac{2}{5}$. The probability that the product is odd is $(\frac{2}{5})^n$. Thus,the probability that the product ends in $2, 4, 6,$ or $8$ is the probability that the product is even and not a multiple of $5$,which is $(\frac{4}{5})^n - (\frac{2}{5})^n = \frac{4^n - 2^n}{5^n}$.

If $n$ positive integers are taken at random and multiplied together,the probability that the last digit of the product is $2, 4, 6$ or $8$ is:

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