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.

Question

2 months ago

13

How many possible sequences of rolls could there have been? (For example, $3,2,3,1,3,2$ is one possible sequence.)

1 answer:

Leona [12.6K] · Answer 1 · 2026-02-24T19:44:10+03:00

Response:

$Sequence = 120$

Step-by-step breakdown:

Provided

6 rolls of a die;

Needed

Find out the potential sequence of rolls.

From the problem, we recognize that three possible outcomes arise when rolling the die;

The potential outcomes are any of the following numbers: 1, 2, or 3.

Total Rolls = 6.

Potential outcomes = 3.

We then calculate the possible rolling sequences by dividing the factorial of the given parameters as follows;

$Sequence = \frac{6!}{3!}$

$Sequence = \frac{6 * 5 * 4* 3!}{3!}$

$Sequence = 6 * 5 * 4$

$Sequence = 120$

Thus, there exist 120 possible sequences of rolls.