The game of Yahtzee is played with five fair six-sided dice. A turn consists of rolling all five dice, selecting the ones you want to keep, re-rolling the rest, and then doing this one more time, if necessary. You need to match certain conditions in order to score points.
(For convenience, you may assume that the dice are all different colors.)

Suppose you roll the 5 dice seeking to get as many sixes as possible. how many ways can you get exactly 3 sixes on the first roll?

How would I do this? Factorials?

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1. For convenience you may assume the dice are different colors. Suppose you roll the 5 dice seeking to get as many sixes as possible. how many ways can you get exactly 3 sixes on the first roll?
How many ways can you get at least 3 sixes on the first roll?
Suppose you only got 1 six on the first roll so you keep it and roll the remaning 4 dice. how many ways can you get at least one six on the last roll?

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2. a) SSSNN
SSNSN
SSNNS
SNSSN
SNSNS
SNNSS
NSSSN
NSSNS
NSNSS
NNSSS
Are there any others?
Is this the same as 5!/3!2!

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👤
bobpursley

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