Answer:
There are 5040 ways he get 3 fours, 5 sixes, and 1 two.
Step-by-step explanation:
Given : A person rolls a standard six-sided die 9 times.
To find : In how many ways can he get 3 fours, 5 sixes, and 1 two?
Solution :
A person rolls a standard six-sided die 9 times.
So, total number of ways die roll is 9! ways.
In die 4 comes 3 times.
So, ways of getting 4 is 3!
In die 6 comes 5 times.
So, ways of getting 6 is 5!
In die 2 comes 1 times.
So, ways of getting 2 is 1!
Total number of ways is given by,
[tex]T=\frac{10!}{3!\times 5!\times 1!}[/tex]
[tex]T=\frac{10\times 9\times 8\times 7\times 6\times 5!}{3\times 2\times 5!\times 1}[/tex]
[tex]T=10\times 9\times 8\times 7\times[/tex]
[tex]T=5040[/tex]
Therefore, there are 5040 ways he get 3 fours, 5 sixes, and 1 two.
