When rolling a pair of standard 6-sided dice, the total outcome can range from 2 to 12. Each total corresponds to a specific number of combinations that can yield that result. Here’s a breakdown of how many different ways each total can occur:
- Total = 2: 1 combination (1+1)
- Total = 3: 2 combinations (1+2, 2+1)
- Total = 4: 3 combinations (1+3, 2+2, 3+1)
- Total = 5: 4 combinations (1+4, 2+3, 3+2, 4+1)
- Total = 6: 5 combinations (1+5, 2+4, 3+3, 4+2, 5+1)
- Total = 7: 6 combinations (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
- Total = 8: 5 combinations (2+6, 3+5, 4+4, 5+3, 6+2)
- Total = 9: 4 combinations (3+6, 4+5, 5+4, 6+3)
- Total = 10: 3 combinations (4+6, 5+5, 6+4)
- Total = 11: 2 combinations (5+6, 6+5)
- Total = 12: 1 combination (6+6)
To summarize, the number of combinations that yield each total is:
- 2: 1
- 3: 2
- 4: 3
- 5: 4
- 6: 5
- 7: 6
- 8: 5
- 9: 4
- 10: 3
- 11: 2
- 12: 1
This shows a symmetry around the total of 7, which has the highest number of combinations. As you move away from 7 in either direction, the number of combinations decreases.