Helpful math reference sheet breaking down permutation formulas for scenarios with and without repetition.

- For problem 1: Since repetition is allowed and we are arranging all 5 distinct letters of "MAINE", the number of arrangements is 5^5 = 3125.
- For problem 2: We are choosing 3 digits from 10 single-digit whole numbers (0-9) without repetition, so n=10 and r=3. Using the formula nPr = n! / (n-r)!, we get 10! / 7! = 10 × 9 × 8 = 720.
- For problem 3: We are arranging 3 distinct people in 3 distinct positions (1st, 2nd, 3rd). Since n=r=3, we use n! = 3! = 6.
- For problem 4: We are choosing 4 students out of 8 to sit in 4 distinct seats, so n=8 and r=4. Using the formula nPr = n! / (n-r)!, we get 8! / 4! = 8 × 7 × 6 × 5 = 1680.