If 3 dice are thrown, in how many ways can we obtain a sum of 12? Please explain step by step and the easiest method to solve this?
6, 5, 1
6, 4, 2
6, 3, 3
5, 5, 2
5, 4, 3
Carry on from here.
Thank you very much
You're very welcome.
Sorry so do you know the answer to this question? I got 25 possibilities. Is this correct?
To find the number of ways to obtain a sum of 12 when throwing 3 dice, we can break down the problem into smaller parts. Let's solve it step by step.
Step 1: Recognize the possible outcomes
Start by identifying the potential values each dice can take on. Since a regular die has 6 faces numbered from 1 to 6, the possible values for each dice are 1, 2, 3, 4, 5, and 6.
Step 2: List down the possible combinations
To find the number of ways to obtain a sum of 12, we need to list all the possible combinations of numbers that can add up to 12 when three dice are thrown.
Here's a list of all the possible combinations:
1 + 5 + 6
1 + 6 + 5
2 + 4 + 6
2 + 6 + 4
3 + 3 + 6
3 + 4 + 5
3 + 5 + 4
3 + 6 + 3
4 + 2 + 6
4 + 3 + 5
4 + 5 + 3
4 + 6 + 2
5 + 1 + 6
5 + 3 + 4
5 + 4 + 3
5 + 6 + 1
6 + 1 + 5
6 + 2 + 4
6 + 4 + 2
6 + 5 + 1
Step 3: Count the total combinations
The number of ways to obtain a sum of 12 is the count of all the combinations listed above. In this case, there are 20 different combinations.
So, the answer is:
There are 20 ways to obtain a sum of 12 when throwing 3 dice.