Four die are rolled. The number of ways in which atleast one die shows `3`, is
(a) 625 (b) 671 (c) 1256 (d) 1296

Options

A. 625
B. 671
C. 1256
D. 1296

Answer

To solve the problem of finding the number of ways in which at least one die shows `3` when rolling four dice, we can follow these steps:

### Step 1: Calculate the total number of outcomes when rolling 4 dice.
Each die has 6 faces, so when rolling 4 dice, the total number of outcomes is calculated as:
\[ 6^4 = 1296 \]

### Step 2: Calculate the number of outcomes where no die shows `3`.
If we want to find the outcomes where no die shows `3`, we can only use the numbers `1, 2, 4, 5, 6`. This gives us 5 options for each die. Therefore, the number of outcomes where no die shows `3` is:
\[ 5^4 = 625 \]

### Step 3: Use the complement principle to find the number of outcomes where at least one die shows `3`.
To find the number of outcomes where at least one die shows `3`, we subtract the number of outcomes where no die shows `3` from the total number of outcomes:
\[ \text{At least one die shows 3} = \text{Total outcomes} - \text{No die shows 3} \]
\[ = 1296 - 625 = 671 \]

### Conclusion
The number of ways in which at least one die shows `3` is **671**.