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A standard six-sided die is rolled 6 times. You are told that among the rolls, there was one 1, two 2's, one 3, and two 4's. How many possible sequences of rolls could there have been?

 Jul 4, 2021
 #1
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The number of possible sequences is 108.

 Jul 4, 2021
 #2
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permutations of {1, 2, 2, 3, 4, 4} ==6!/(2!)(2!)==720 / 4 ==180 sequences of rolls

 Jul 4, 2021
 #3
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we can make it simple from an example like if we toss a coin we can get 2 possible outcome

if

 we toss 2 coin we can get 2 * 2 possible outcome

 if we toss 3 coin we can get 2* 2 *2  possible outcomes 

so tossing a dice 6 times is same as tossing 6 dice one time. 

for one fair dice the possible no of outcome is 6  {1,2,3,4,5,6}

for 2 dice possible outcomes 6*6 

for 3 dice possible outcomes 6*6 *6

for 4 dice possible outcomes 6*6*6*6 

for 5 dice possible outcomes 6*6*6*6*6

for 6 dice possible outcomes 6*6*6*6*6*6  = 6 ^6             [answer]

 Jul 5, 2021

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