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We need a sum of 20. This can be achieved in the following ways : {5,5,5,5} --> 1 way {5,5,4,6} --> 4!/(2!) ways = 12 {4,4,6,6} --> 4!/(2!2!) ways = 6 ways {3,5,6,6} --> 4!/2! ways = 12 ways {2,6,6,6} --> 4!/3! ways = 4 ways

Total ways = 6x6x6x6

So probability = 35/1296 ... Answer (a) _________________

This question doesn't require any complex math at all; it can be solved with some arithmetic, some 'brute force' and a bit of logic:

To start, each of the 4 dice has 6 possible outcomes (1, 2, 3, 4, 5 and 6), so there are 6^4 = 36^2 = 1296 total outcomes. Thus, the correct answer is either a fraction out of 1296 or a fraction that has been reduced from 1296. This allows you to immediately eliminate answers C, D and E.

From the two remaining answers, there are either 35 or 55 dice combinations that will total 20. Using a bit of 'brute force', we can name the groups:

6662 6653 6644 6554 5555

Each of these groups has a certain number of possible outcomes. For example, 5555 can only occur 1 time, while 6662 can occur 4 times (2666, 6266, 6626 and 6662). At this point, you should note that 2 of the 5 possibilities yield just 1+4 = 5 options, so it's highly likely that the total number of possibilities is relatively small (in this case, 35 and not 55). If you wanted to list out all of the possibilities, then you could (and there would be 35 of them). If you 'time' your work, you could probably complete this step in 1-2 minutes.