Question

Many cars have keyless entry. To open the lock, you may press a 5-digit code on a set of buttons like that illustrated. The code may include repeated digits like 11433 or 55512. 1-2 3-4 5-67-8 9-0 a) How many different 5-digit codes can be made using the 10 digits if repetition is permitted?

Answer 1

The number of different 5-digit codes that can be made using 10 digits with repetition permitted is 100,000, calculated using the permutation formula with repetition (10 to the power of 5).

Step-by-step explanation:

To determine the number of different 5-digit codes that can be made using the 10 digits (0-9) with repetition permitted, we simply raise the number of possible choices for each digit to the power of the number of digits in the code. Since there are 10 possible digits for each position, and there are 5 positions in the code, we use the formula for calculating permutations with repetition allowed:

Number of 5-digit codes = 105 = 10 × 10 × 10 × 10 × 10 = 100,000.

Thus, there are a total of 100,000 different 5-digit codes possible when duplicates of digits are permitted.