If three different dice are rolled, then the number of ways in which the largest of three numbers is not 4 is equal to

Explanation

Here, sample space `= 6^3 = 216`

Below are the cases when `4` is the largest number.

`Case 1:` When one of the dice contains `4` and other two dice contains any of the numbers `1,2,3`.

Total number of ways in this case `= C(3,1)**3!**3! = 27`

`Case 2:` When two of the dice contains `4` and third dice contains any of the numbers `1,2,3`.

Total number of ways in this case `= C(3,2)**3! = 9`

`Case 3:` When all of the dice contains `4`.

Total number of ways in this case `= 1`

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