Question

A park bench can seat 3 people. How many seating arrangements are possible if 3 people out of a group of 12 want to sit on the park bench?

Answer 1

Since the word 'arrangements' is emphasized we have to consider that order of seating is also important, that is why we took the example of arrangements of A, B, C in order of 3. we have 6 possible arrangements- ABC, ACB, BCA, BAC, CBA, and CAB. If the order was not important then there is only one way(ABC) of seating 3 people on the bench per each group of 3, i.e. 220 ways of seating 220 groups of 3 people on the bench.

But since seating order is important the no. of seating arrangements is 1320.