Question

A standard six-sided die is rolled 6 times. You are told that among the rolls, there was one 1, two 2's, and three 3's. How many possible sequences of rolls could there have been? (For example, 3,2,3,1,3,2 is one possible sequence.)
I tried this and I still don't get it. PLEASE HELP

Answer 1

Answer:

Step-by-step explanation:

Exactly two numbers appear:

There are  

(

6

2

)

(62)

ways for two of the six numbers to appear. On each of the six rolls of the die, there are two possible outcomes, giving  

(

6

2

)⋅

2

6

(62)⋅26

possible outcomes in which two of the six numbers appear. However, of these  

2

6

26

sequences, there are two in which the same number is rolled six times. Thus, the probability of exactly two numbers appearing in six rolls of the die is  

(

6

2

)⋅(

2

6

−2)

6

6

Answer 2

Answer:

34

Step-by-step explanation: