Solve the problem.
-How many three-digit numbers have the sum of their digits equal to 20?
A)30
B)40
C)36
D)32

Question

Quizplus · Accepted Answer

To find three-digit numbers whose digits sum to 20, we can use combinatorics, considering the problem as distributing 20 identical items into 3 distinct boxes (digits), where each box can hold between 1 and 9 items (since a digit can be 1-9, and the first digit cannot be 0 for a three-digit number). This is a variation of the stars and bars method, adjusted for the constraints. The direct calculation for this specific problem is complex due to the constraints on digit values, so a more practical approach involves enumerating possibilities or using programming. However, the correct enumeration, considering the constraints (especially that the first digit cannot be 0 and each digit must be between 0 and 9), gives us 36 valid combinations.

Solve the Problem. -How Many Three-Digit Numbers Have the Sum of Their Digits