Amateur wrote:

What is the probability that you will get a sum of 8 when you throw three dice simultaneously?

Similarly, What is the probability that you will get a sum of 22 when you throw four dice simultaneously?

What is the probability that you will get a sum of 8 when you throw three dice simultaneously?This sum of 8 can occur in the following cases:

1-1-6 --> 3!/2!=3 ways;

1-2-5 --> 3!=6 ways;

1-3-4 --> 3!=6 ways;

2-2-4 --> 3!/2!=3 ways;

2-3-3 --> 3!/2!=3 ways.

Total of 3+6+6+3+3=21 ways.

Now, since the total number of outcomes is 6^3, then the probability is 21/6^3.

What is the probability that you will get a sum of 22 when you throw four dice simultaneously?This sum of 22 can occur in the following cases:

6-6-6-4 --> 4!/3!=4 ways;

6-6-5-5 --> 4!/(2!2!)=6 ways.

Total of 4+6=10 ways.

Now, since the total number of outcomes is 6^4, then the probability is 10/6^4.

Hope it's clear.

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