An office manager must choose a five-digit lock code for the office door. The first and last digits of the code must be odd, and no repetition of digits is allowed. How many different lock codes are possible?

6720 lock codes

Explanation:

The numbers to be chosen from are:

0 1 2 3 4 5 6 7 8 9

The odd numbers are five in number which are: 1 3 5 7 9

The even numbers are five in number which are: 0 2 4 6 8

If the first number is odd, therefore, it can be chosen in five ways

After the first number is chosen, there are 4 left odd numbers so the last number can be chosen in four ways.

There are 8 left numbers after they are chosen, so the second number can be chosen in eight ways

Third number can be chosen similarly, in seven ways

Fourth number can be chosen in six ways

Hence, the number of different combinations are:

5*4*8*7*6 = 6720 combinations