Final answer:
The number of different 5-digit codes possible without repetition and with the first digit not being zero is 27,216. This is calculated by multiplying the number of choices for each digit.
the correct answer is:
c. 90,000
Step-by-step explanation:
To determine how many different 5-digit codes are possible under the condition that repetition of digits is not allowed and the first digit cannot be zero, we must calculate the number of permutations given these restrictions. The first digit can be any number from 1 to 9, giving us 9 options. For each subsequent digit, the number of options decreases by one since repetition is not allowed, thus for the second digit, we have 9 options (0 can be used but the first digit already used one option), for the third digit we have 8 options, for the fourth we have 7, and for the fifth, we have 6 options left.
Therefore, the total number of different 5-digit codes can be calculated by multiplying the number of options for each position: 9 × 9 × 8 × 7 × 6, which equals 27,216.
This calculation is based on the fundamental counting principle, which allows us to multiply the number of ways each independent choice can be made to find the total number of different combinations.