A pair of dice thrown. If the two numbers appearing on them are different, find the probability
(i) the sum of the numbers is `6`
(ii) the sum of the numbers is `4` or less
(iii) the sum of the number is `4`.

Explanation

To solve the problem of finding the probability of different sums when a pair of dice is thrown, we will follow these steps:

### Step 1: Determine the Total Outcomes
When two dice are thrown, the total number of outcomes is \(6 \times 6 = 36\). However, since we are only considering outcomes where the two numbers are different, we need to exclude the outcomes where both dice show the same number.

The pairs where both numbers are the same are:
- (1, 1)
- (2, 2)
...