The combination lock on a suitcase has 3 wheels. Each wheel has 10 positions. How many different combinations are possible?

1 answer

To determine the total number of different combinations possible for a combination lock with 3 wheels where each wheel has 10 positions, we can use the counting principle.

Each wheel can be independently set to any of the 10 positions. Therefore, for each wheel, there are 10 choices.

Since there are 3 wheels, the total number of combinations can be calculated by multiplying the number of choices for each wheel together:

\[ \text{Total Combinations} = \text{Choices for Wheel 1} \times \text{Choices for Wheel 2} \times \text{Choices for Wheel 3} \]

This gives:

\[ \text{Total Combinations} = 10 \times 10 \times 10 = 10^3 = 1000 \]

Thus, the total number of different combinations possible is

\[ \boxed{1000} \]