Yahtzee! Part 1

Discrete Mathematics Level pending

In the game of Yahtzee, each player's turn consists of rolling five 6-sided dice. The highest possible score is obtained when a player rolls all five dice as the same number. Whenever this happens, this is called a "Yahtzee" (hence the name of the game).

During each player's turn, that player may re-roll the dice up to two more times after the first roll. However, we will ignore this rule for this problem.

If the probability of rolling a Yahtzee in the first roll is \(\frac{a}{b}\), where \(a\) and \(b\) are positive co-prime integers, then what is \(a+b\)?

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