Consider the game Yahtzee and a single roll of 5 dice. For this problem, assume
ID: 2923266 • Letter: C
Question
Consider the game Yahtzee and a single roll of 5 dice. For this problem, assume the order of the dice does not matter. Thus, ultimately, each roll corresponds to choosing r = 5 items (dice) from as set of n = 6 values. Thus, the total number of dierent rolls possible is given by the formula n+r1 r =10 5= 252. For the following questions, re-apply this formula where applicable and simplify your answers to decimal form. (a) How many dierent rolls have no repeated value (they are all unique)? (b) How many dierent rolls correspond to a full house? (c) How many dierent rolls correspond to a large straight? (d) How many dierent rolls correspond to a small straight but not a large straight? (e) How many dierent rolls have exactly three 5’s? (f) How many dierent rolls contain a three-of-a-kind, but not a 4-of-a-kind?
Note: Since the order does not matter in this question, the answers do not reect the probability of these various outcomes. This will be done in the next assignment.
Explanation / Answer
This means that there are 14 different ways that five dice can give us a small straight. Of the 14 distinct ways to obtain small straights, only two of these {1,2,3,4,6} and {1,3,4,5,6} are sets with distinct elements. There are 5! = 120 ways to roll each for a total of 2 x 5! = 240 small straights