How many unique ways can 10 people fit on a 4-person park bench?

Answer 1

To determine how many unique ways 10 people can fit on a 4-person park bench, we use the concept of permutations since the order of seating matters. We can select 4 people from the 10 in ( \binom{10}{4} ) ways, and then arrange those 4 people in ( 4! ) ways. Therefore, the total number of unique arrangements is given by ( \binom{10}{4} \times 4! = \frac{10!}{(10-4)!} = \frac{10!}{6!} = 5040 ). Thus, there are 5,040 unique ways for 10 people to fit on a 4-person park bench.