Question

Four processes are involved in assembling a certain product and they can be preformed in any order. The management wants to test each order to determine which is the least time consuming. How many different orders will have to be tested?

Answer 1

24

Explanation:

there are 4 processes.

you need 4 blanks.

_ _ _ _

you have 4 choices to pick from for the first blank

for the second, 3

the third, 2

and the last, 1

so you have 4! or 4 factorial.

you take 4*3*2*1 = 24

Answer 2

The first process can be any one of the 4. For each of those ...
The second process can be any one of the remaining 3. For each of those ...
The third process can be either of the remaining two. For each of those ...
The fourth process will be the only 1 left.

The total number of ways to order them is (4 x 3 x 2 x 1) = 24 orders.