Question

How many different 5-digit codes are possible using the keypad shown at the right if the first digit cannot be 0 and no digit may be used more than once?

Short answer

The number of possible 5-digit codes are87120.

Step-by-step solution

Step 1. Given Information.

It is to be determined how many different 5-digit codes are possible using the keypad shown if the first digit cannot be 0 and no digit may be used more than once.

Step 2. Calculation.

There are 12 digits on the keypad.

If the first digit cannot be 0, there are 11 ways to select the first digit.

Now 11 digits are left to be selected for the second digit.

Then 10, then 9 and then 8.

By the Fundamental Counting Principle, there are $11\times 11\times 10\times 9\times 8=87120$ different ways to select the 5-digit code.

Step 3. Conclusion.

Hence, the number of possible 5-digit codes are 87120.