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Now, for the numerator = total outcomes(which is 6^5) - number of outcomes where all four dice show different numbers (which is 6*5*4*3) -number of outcomes where all show same number (which is 6) = 7776-360 -6 = 7410

Prob is 7410/7776 = 3705/3888. I dont think I am sure of this one. OA pls.

The probability of obtaining at least four "sixes" when rolling five dice is as per Paul's solution that is, C(5,4)*5/(6^5). However, there are six marks on each dice {1,2,3,4,5,6} so that ans is

Oxon, you are right, I forgot to consider that there are 6 possible values (1,2,3,4,5,6) that could be same and also when all 5 are same!
Hence, it should be:
[(1/6)^4 * 5/6 * 5C4 + (1/6)^5] * 6 = 26/6^4 = 13/648
You are absolutely right _________________