Question

How many outcome sequences are possible when a die is rolled 4 times where we say for instance that the outcome is 3 4 3 1 if the first roll landed on 3 the second on 4 the third on 3 and the fourth on 1

Answer 1

the possible outcome sequences when a die is rolled 4 times is 1296

Explanation:

Given the data in the question;

a die is rolled 4 times

and outcomes are { 3, 4, 3, 1 }

we know that; possible number of outcomes on a die is n = 6{ 1,2,3,4,5,6 }

Now when we roll a die lets say, r times

then the total number of possible outcomes will be;

N =
`n^r`

given that; r = 4

Hence if we roll a die 4 times;

Total number of possible outcome N = 6⁴

N = 1296

Therefore, the possible outcome sequences when a die is rolled 4 times is 1296