What is the probability of getting a sum of 22 or more when four dice are thrown?Choices:- 6/432 5/432 4/1296 6/1296

The probability of getting a sum of 22 or more when four dice are thrown is 6/1296.

Here's the step-by-step explanation:

1. The maximum sum that can be obtained by throwing four dice is 24 (6+6+6+6).

2. The sums that are 22 or more are 22, 23, and 24.

3. We need to find the number of ways these sums can be obtained.

   • For a sum of 22, the possible combinations are (6,6,6,4), (6,6,5,5), and their permutations. There are 21 permutations for (6,6,6,4) and 6 permutations for (6,6,5,5). So, there are a total of 27 ways to get a sum of 22.

   • For a sum of 23, the possible combinations are (6,6,6,5) and its permutations. There are 21 permutations for this combination. So, there are 21 ways to get a sum of 23.

   • For a sum of 24, the only combination is (6,6,6,6). There is only 1 way to get this sum.

4. So, the total number of ways to get a sum of 22 or more is 27 (for 22) + 21 (for 23) + 1 (for 24) = 49.

5. The total number of outcomes when four dice are thrown is 6^4 = 1296 (since each die has 6 faces and there are 4 dice).

6. Therefore, the probability of getting a sum of 22 or more is the number of favorable outcomes divided by the total number of outcomes, which is 49/1296.

However, none of the given options match this result. There might be a mistake in the question or the provided options.