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 only combinations are (6,6,6,4), (6,6,5,5), and their permutations. There are 4!/(3!1!) = 4 ways for the first combination and 4!/(2!2!) = 6 ways for the second combination. So, a total of 10 ways.

   • For a sum of 23, the only combinations are (6,6,6,5), and its permutations. There are 4!/(3!1!) = 4 ways.

   • For a sum of 24, the only combination is (6,6,6,6), which is just 1 way.

4. So, the total number of favorable outcomes is 10+4+1 = 15.

5. The total number of outcomes when four dice are thrown is 6^4 = 1296.

6. Therefore, the probability is 15/1296 = 5/432.

So, the correct answer is 5/432.