Question

A boy found a bicycle lock for which the combina- tion 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 1

4096 possible combinations

Explanation:

If a experiment can takes place in forms n1, then a second experiment can takes place in forms n2, ... , then a i-experiment can takes place in ni forms finally the number of possibilities to carry out the entire experiment are :

n1 x n2 x ... x ni

This is call the multiplication principle.

In our experiment (finding a four - digit number)

d1 can be chosen between 1,2,3,4,5,6,7,8

d2 can be chosen between 1,2,3,4,5,6,7,8

.

.

.

d4 can be chosen between 1,2,3,4,5,6,7,8

The lock combinations are d1 x d2 x d3 x d4 = 8 x 8 x 8 x 8 = 8^4 = 4096