Question

A combination lock like the one shown has three dials. Each of the dials has numbers ranging from 1 to 8. How many different combinations are possible with the lock?

512 combinations
343 combinations
24 combinations
48 combinations

Answer 1

512.

Explanation:

First there is 111, 222 ...... 888.

There are 8 of these.

Then there are the number of ways you can arrange numbers when 2 of them are the same

= 8P3/2

= 168

Finally if all numbers are different the number of ways

= 8P3 = 336

Answer is 8 + 168 + 336

= 512.