Question

For a TV talent show, there are three celebrity judges already chosen plus two judges that need to be selected from an audience of 200 people. How many seating arrangements are there for five judges? (the 3 celebrity judges and 2 chosen judges). Explain your solution. (Hint: This involves both a permutation and a combination)

Answer 1

Solution :

There are five judges ( 3 are celebrities and 2 are from audience ). Also if there is not any condition on seating ( like 3 celebrities are together or what else ) then that means any one of 5 judges can sit anywhere among 5 seats.

In this situation there are 5 judges and 5 seats available.

For first judge there are 5 choices to sit. Second has 4 choices to sit. Third has 3 choices to sit. Fourth has 2 choices to sit. And fifth has only one seat available to sit.

The multiplicative principal of counting states that if there are "m" ways to do one thing and "n" ways to do another thing then there are "m*n" ways to do both the things together.

Using this multiplicative principle we get, there are total 5*4*3*2*1 = 120 arrangements in which these 5 judges can sit.