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Plz help

 

A standard six-sided die is rolled 7 times.  You are told that among the rolls, there was one 1, two 2's, and three 4's.  How many possible sequences of rolls could there have been?  (For example, 5, 1, 2, 2, 4, 4, 4 is one possible sequence.  4, 1, 4, 4, 2, 1, 1 is one possible sequence.)

 Mar 25, 2023
 #1
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1,2,2,3,4,4,4=7!/3!2! ==420 permutations
1,2,2,4,4,4,5=7!/3!2! ==420 permutations
1,2,3,4,4,4,6=7!/3!2! ==420 permutations


420 x 3 ==1,260 possible sequences of rolls

 Mar 26, 2023
 #2
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You started with the right idea, but you have to do it for all 6 digits:

 

1122444=7!/3!2!2! =210
1222444=7!/3!3! =140
1223444=7!/3!2! = 420
1224444 =7!/4!2! = 105
1224445 =7!/3!2! = 420
1224446 = 7!/3!2! = 420
The total =210+140+420+105+420+420==1715 possible sequences of rolls

 Mar 26, 2023

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