Question 1207575: A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, 4, 6, 6, 1, 5 is one possible sequence.)
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
A standard six-sided die is rolled 7 times. You are told that among the rolls, there was one 1, one 2,
one 3, one 4, one 5, and two 6's. How many possible sequences of rolls could there have been?
(For example, 2, 3, 4, 6, 6, 1, 5 is one possible sequence.)
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In 1st position, any number from 1 to 6 inclusive, can be.
In 2nd position, any number from 1 to 6 inclusive, can be.
In 3rd position, any number from 1 to 6 inclusive, can be.
In 4th position, any number from 1 to 6 inclusive, can be.
In 5th position, any number from 1 to 6 inclusive, can be.
In 6th position, any number from 1 to 6 inclusive, can be.
In 7th position, any number from 1 to 6 inclusive, can be.
The numbers in i-th position are independent on the numbers in j-th position.
From it, it is obvious, that the number of all possible sequences is  = 279936. ANSWER
Solved.
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