Question

In the game Yahtzee, five dice are tossed simultaneously. Recall that it is helpful to think of the dice as distinct – e.g., dice 1, dice 2, . . ., dice 5. a. How many different outcomes are possible? b. How many outcomes show the same number (a Yahtzee!)? c. How many contain a three-of-a-kind (three dice show the same number x, the other two show numbers different from x; e.g., (2, 2, 3, 2, 4) or (3, 4, 3, 4, 4), etc.)? d. How many form a large straight (the five numbers that show up can be consecutively ordered)? e. How many contain two 2's, one 4, two 6's?

          In the game Yahtzee, five dice are tossed simultaneously. Recall that it is helpful to think of the dice as distinct – e.g., dice 1, dice 2, . . ., dice 5.

a. How many different outcomes are possible?
b. How many outcomes show the same number (a Yahtzee!)?
c. How many contain a three-of-a-kind (three dice show the same number x, the other two show numbers different from x; e.g., (2, 2, 3, 2, 4) or (3, 4, 3, 4, 4), etc.)?
d. How many form a large straight (the five numbers that show up can be consecutively ordered)?
e. How many contain two 2's, one 4, two 6's?

Added by Christine C.

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