Answer to Question #117095 in Combinatorics | Number Theory for Priya

Question

There are 5 chairs in a row, and three people. In how many ways can you place the people on the chairs? (each person must occupy exactly one chair, so that two chairs will remain free.)

Answer 1

Answer: 60

Method 1

Number of ways 5 seats can be grouped as 3 seats= C⁵₃=10

Number of arrangement within each group of 3 seats= 3!=6

Therefore total number of ways three people can seat in five seats = 10*3! =60

Method 2

Number of ways one person can seat in 5 seats = 5

Number of ways second person can seat after the first person has occupied a seat = 4

Number of ways third person can seat after first and second persons have occupied two seats = 3

Therefore, total number ways three people can seat in five seats = 5*4*3 = 60