# A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$

###### Question:

## Answers

There are 6*5*4 = 120 ways to choose the positions of the 3's. Then there are 3 ways to choose the position of the 1, and the remaining rolls must be 2, so there are 120*3 = 360 possible sequences.

[tex]Sequence = 120[/tex]

Step-by-step explanation:

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

[tex]Sequence = \frac{6!}{3!}[/tex]

[tex]Sequence = \frac{6 * 5 * 4* 3!}{3!}[/tex]

[tex]Sequence = 6 * 5 * 4[/tex]

[tex]Sequence = 120[/tex]

Hence, there are 120 possible sequence.