you roll each die and find the sum. how many different sums are possible?

Explanation:

Step1: Determine minimum sum

The minimum value on a single - die is 1. For three dice, the minimum sum is $1 + 1+1=3$.

Step2: Determine maximum sum

The maximum value on a single - die is 6. For three dice, the maximum sum is $6 + 6+6 = 18$.

Step3: Count the number of possible sums

The possible sums range from 3 to 18. The number of integers from $a$ to $b$ (where $a$ and $b$ are integers and $b\geq a$) is given by $b - a+1$. Here, $a = 3$ and $b = 18$, so the number of different sums is $18 - 3+1=16$.

Answer:

16