Question

QUESTION: There are 20 students in a class. The classroom in which the class is held has 90 seats in a single row facing the blackboard and the podium. We want to seat the 20 students in this row of 90 seats so that they maintain proper social distancing: there must be at least 2 empty seats between any two students. For example, if we only had 3 students and a row of 10 seats, then

+s2 + +s1 + + + +s3

is a valid way of seating. Here s1, s2, s3 are the three students, and + denotes an empty seat. Find the number of ways of seating the 20 students among the 90 seats so that social distancing is followed, i.e. there are at least 2 empty seats between any two students.

Answer 1