Chef and his Tuition

Mr. Chef recently started giving tuitions on Computer Programming to $N$ students and the fee was $X$ per student. Mr. Chef is a spendthrift, so in order to control his spending habits, he thought of a plan. He decided to give each student a due date $D$i at random between $1$ and $20$ of the month, so that he could receive some amount of money throughout the month. He also told the students that