Mathematical Foundation (Discrete Structures) (Counting)

Exercises Problem 1. How many ways are there to distribute 10 bonus points to three students? Problem 2. How many ways are there to distribute 100 bonus points to 30 students? Problem 3. How many 5-digit phone numbers are there in which the digits do not decrease (i.e., every digit is greater than or equal to the previous one)? Problem 4. How many ways are there to distribute 100 bonus points to 30 students so that each student receives at least 3 points? Instructions Complete the following problems by filling in the blanks. Blanks permit strings (i.e., an ordered set of one or more characters). Amounts should be represented with the fewest characters or most legible format possible (e.g., use (1) instead of 1365, but use 10 in lieu of ())