Three different dice are rolled simultaneously three times. The probability that all of them show different numbers only two times, is equal to

When three different dice are rolled, the probability that they show different numbers is 6/6 * 5/6 * 4/6 = 5/9. The probability that they do not all show different numbers is 1 - 5/9 = 4/9. Using the binomial distribution for exactly 2 successes in 3 trials, the probability is 3C2 * (5/9)^2 * (4/9)^1 = 3 * 25/81 * 4/9 = 300/729. Simplifying the fraction by dividing the numerator and denominator by 9 gives the result 175/324.

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