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) How many ways can you roll all the dice? (ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points? (iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this?
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) How many ways can you roll all the dice?
(ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points?
(iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this?
(iv) Suppose instead you are trying to get your dice to roll 4 consecutive numbers (ex. (1, 2, 3, 4, 1) or (2, 3, 4, 5, 3)) How many different ways are there to do this? (make sure to not count any only consecutive numbers)
This is a combinatorics math counting problem.
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