You know telephone extension number is 666 but you forgotten The last 4 digits

Question

You know that the extension of a private telephone number is 666, but you have forgotten the last 4 digits. You can only recall that the last 4 digits are 1, 3, 5, and 7, but you do not know the order. What is the maximum number of telephone calls you will need to make in order to dial the correct number?

Answer 1

The four digits 1, 3, 5 and 7 may appear in 4*3*2*1 = 24 different arrangements.  There are four choices for the first digit, then 3 remain for the second digit, then 2 for the third, then 1 for the last.

 

For learning, it helps to enumerate them:

1 3 5 7
1 3 7 5
1 5 3 7
1 5 7 3
1 7 3 5
1 7 5 3
3 1 5 7
3 1 7 5
3 5 1 7
3 5 7 1
3 7 1 5
3 7 5 1
5 1 3 7
5 1 7 3
5 3 1 7
5 3 7 1
5 7 1 3
5 7 3 1
7 1 3 5
7 1 5 3
7 3 1 5
7 3 5 1
7 5 1 3
7 5 3 1

 

Answer 2

Assuming that you can tell whether the order correct only after you have been dialed all four,

4!