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Plz help with this I need it

 

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 27, 2023
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(1, 1, 2, 2, 4, 4, 4)==7! / (3!2!2!)==210 permutations

(1, 2, 2, 2, 4, 4, 4)==7! / (3!3!)   ==140 permutations

(1, 2, 2, 3, 4, 4, 4)==7! / (3!2!)   ==420 permutations

(1, 2, 2, 4, 4, 4, 4)==7! / (4!2!)   ==105 permutations

(1, 2, 2, 4, 4, 4, 5)==7! / (3!2!)   ==420 permutations

(1, 2, 2, 4, 4, 4, 6)==7! / (3!2!)   ==420 permutations

 

Total =210 + 140 + 420 + 105 + 420 + 420==1,715 possible sequences of rolls.

 Mar 27, 2023

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