BTGmoderatorLU wrote:How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?

A. 8
B. 12
C. 60
D. 118
E. 120

The number of choices for a seat the first person could have is 5. Once he has sat down, the number of choices for a seat the second person could have is 4. Finally, the number of choices for a seat the third person, after the first two have sat down, could have is 3. Thus, the number of ways 3 people can sit a table of with five seats is:

5 x 4 x 3 = 60

Alternate Solution:

The number of seats to be occupied can be selected in 5C3 = 5!/(3!*2!) = (5x4)/2 = 10 ways.

Once the seats to be occupied are determined, there are 3! = 6 ways the three people can be arranged in those seats.

In total, there are 10 x 6 = 60 ways the three people can sit at a table of five seats.

Answer: C