Problem: Compute the number of distinct ways in which 77 one-dollar bills can be distributed to 7 people so that no person receives less than $\$ 10$. Solution: Just give each person $10$ dollars first. Now, we have $7$ dollars left over to distribute among $7$ people. This is a distributions problem and is $\binom{7 + 7-1}{7-1} = \binom{13}{6}$.