PROBLEM 1E

A boy found a bicycle lock for which the combination was unknown. The correct combination is a four-digit number, d1d2d3d4, where di, i = 1, 2, 3, 4, is selected from 1, 2, 3, 4, 5, 6, 7, and 8. How many different lock combinations are possible with such a lock?

Answer :

Step 1 of 1:

A boy found a bicycle lock for which the combination was unknown.

The correct combination four-digit number,d.

Where i=1,2,3,4 is selected from 1,2,3,4,5,6,7 and 8.

Then the table is given below.

Combination | |||

8 | 8 | 8 | 8 |

Now we have to find how many different lock combinations are possible with such a lock.

We have 4 places,each has to be filled by one of 1,2,3,4,5,6,7 or 8.

Hence we have 8 different ways to fill each of the four places.

Hence total combinations possible is