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2. The access code for a car's security system consists of four digits. The first digit cannot be zero, and the last digit must be odd. How many different codes are available?

3. The starting lineup for a softball team consists of 10 players. How many different batting orders are possible?



Answer :

GinnyAnswer

Final answer:

To determine the number of different codes for the car's security system, consider the restrictions provided and calculate the total possible combinations within those constraints.


Explanation:

To calculate the number of different codes for the car's security system, we need to consider the restrictions:

  1. The first digit cannot be 0, so it has 9 possibilities (1-9).
  2. The last digit must be odd, providing 5 options (1, 3, 5, 7, 9).
  3. For the two middle digits, they can range from 0 to 9, giving 10 options each.

Therefore, the total number of different codes available is: 9 (for the first digit) 10 (for the second digit) 10 (for the third digit) * 5 (for the fourth digit) = 4,500 codes.


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