In how many ways can 8 persons be seated on a bench if only three seats are available?
Answer Details
The first person has 8 choices for a seat, the second person has 7 choices remaining, and the third person has 6 choices. However, the order in which they choose their seats does not matter, so we need to divide by the number of ways that the three people can be arranged. This is given by 3 factorial (3!), which is 3 x 2 x 1 = 6. Therefore, the total number of ways that 8 persons can be seated on a bench if only three seats are available is:
8 x 7 x 6 / 3! = 336
So the correct answer is (C) 336.