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Five dice of different colors are being rolled simultaneously. The numbers that show up on the...

Five dice of different colors are being rolled simultaneously. The numbers that show up on the faces are added up to compute X. How many different die rolls result in X being divisible by 3?
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Answer #1

Answer is 2*6^4 = 2592

Explanation :

Case1 .. first 4 among 5 dice has sum divisible by 3 hence to get it divisible by 3, 5th die has to be 3 or 6.

possibility is anything on first 4 position in 6^4 ways and the 5th possition in 2 ways. That is totally 2*6^4 ways.

Case2 .. first 4 among 5 dice has sum remainder 1 when we divide by 3, to get it divisible by 3, 5th die has to be 2 or 5.

possibility is anything on first 4 position in 6^4 ways and the 5th possition in 2 ways. That is totally 2*6^4 ways.

Case3 .. first 4 among 5 dice has sum remainder 2 when we divide by 3, to get it divisible by 3, 5th die has to be 1 or 4.

possibility is anything on first 4 position in 6^4 ways and the 5th possition in 2 ways. That is totally 2*6^4 ways.

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