The number of combinations possible with a lock that has 40 numbers and a 3-number combination is:

The number of combinations possible with a lock that has 40 numbers and a 3-number combination is:

• A. 12,000
• B. 16,000
• C. 32,000
• D. 64,000

Answer: (D)

To determine the number of combinations possible with a lock that has 40 numbers and a 3-number combination, it's essential to understand how combinations work in this context. A typical combination lock allows the same number to be used more than once, which means the total number of possible combinations can be calculated using options available for each position in the combination. In this case, each of the three positions in the combination can be filled by any of the 40 numbers. Therefore, for the first number, there are 40 choices. The same applies to the second number and the third number. Since repetitions are allowed, the total number of combinations is calculated by multiplying the number of choices for each position: Total combinations = (Choices for first position) × (Choices for second position) × (Choices for third position) This results in: Total combinations = 40 × 40 × 40 = 40^3 = 64,000 Thus, the number of combinations possible for this lock is 64,000.

To determine the number of combinations possible with a lock that has 40 numbers and a 3-number combination, it's essential to understand how combinations work in this context. A typical combination lock allows the same number to be used more than once, which means the total number of possible combinations can be calculated using options available for each position in the combination.

In this case, each of the three positions in the combination can be filled by any of the 40 numbers. Therefore, for the first number, there are 40 choices. The same applies to the second number and the third number. Since repetitions are allowed, the total number of combinations is calculated by multiplying the number of choices for each position:

Total combinations = (Choices for first position) × (Choices for second position) × (Choices for third position)

This results in:

Total combinations = 40 × 40 × 40 = 40^3 = 64,000

Thus, the number of combinations possible for this lock is 64,000.