Final answer:
To find the number of 4-digit numbers whose digits are non-increasing, we utilize a combination formula with repetition. The calculation using the “choose” method gives us 715 non-increasing 4-digit numbers.
Step-by-step explanation:
The question asks to find the number of 4-digit numbers whose digits are non-increasing. This means that each digit must be the same or less than the one before it. To solve this, we can think of the problem as a combination problem with repetitions allowed. Since there are 10 digits (0-9), and we are forming a 4-digit number, the formula we use is (n + k - 1) choose k, where n is the number of things to choose from, and k is the number we are choosing. In our case, n = 10 and k = 4.
Using the formula, we get (10 + 4 - 1) choose 4, which is 13 choose 4. This can be calculated as 13! / (4! * (13 - 4)!), resulting in a total of 715 non-increasing 4-digit numbers. Therefore, the correct answer is b) 715.