Question

An art class has 10 students in it. All of them must present their portfolios and explain their work to the instructor and their classmates at the end of the term.

How many presentation orders are possible if:

a) the student names are drawn from a hat to determine who goes first, second, and so on?
b) the student names are put in alphabetical order to determine who goes first, second, and so on?

Answer 1

(a) Since each order is chosen in perfectly random manner:

First person is selected in 10 ways

Second person is selected in 9 ways

Third person is selected in 8 ways

Fourth person is selected in 7 ways

Fifth person is selected in 6 ways

Sixth person is selected in 5 ways

Seventh person is selected in 4 ways

Eighth person is selected in 3 ways

Ninth person is selected in 2 ways

Tenth person is selected in 1 way

So,

Number of presentation orders

10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 = 3,628,800

So,

Answer is:

3,628,800

(b)

If the student names are puti n alphabetical order, there is no choice. There is only one way.

So,

Answer is:

1