This is a combinatorics math counting problem: Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once. (i) You are attempting to roll a full house (where 2 dice have the same number and 3 dice have the same different number; ex. (5, 5, 3, 3, 3)). How many ways can you roll a full house? (do not count any rolls where all 5 dice are the same number) (ii) You are now attempting to roll 4 of a kind (4 dice have the same number and the 5th dice has a different number; ex. (1, 1, 1, 1, 6)). How many ways can you roll 4 of a kind? (do not count any rolls where all 5 dice are the same number) (iii) Finally, you only have one section left, to roll 3 of a kind (3 dice have the same number and the last 2 dice have two different numbers; ex. (3, 3, 3, 5, 6)). How many ways can you roll 3 of a kind? (do not count any rolls where all 5 dice are the same number, do not count any full houses, and do not count any 4 of a kinds)
This is a combinatorics math counting problem:
Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once.
(i) You are attempting to roll a full house (where 2 dice have the same number and 3 dice have the same different number; ex. (5, 5, 3, 3, 3)). How many ways can you roll a full house? (do not count any rolls where all 5 dice are the same number)
(ii) You are now attempting to roll 4 of a kind (4 dice have the same number and the 5th dice has a different number; ex. (1, 1, 1, 1, 6)). How many ways can you roll 4 of a kind? (do not count any rolls where all 5 dice are the same number)
(iii) Finally, you only have one section left, to roll 3 of a kind (3 dice have the same number and the last 2 dice have two different numbers; ex. (3, 3, 3, 5, 6)). How many ways can you roll 3 of a kind? (do not count any rolls where all 5 dice are the same number, do not count any full houses, and do not count any 4 of a kinds)
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