Question

An ID at the zoo consists of 3 letters followed by 2 numbers (0-9). How many unique IDs are possible if the numbers and letters CANNOT repeat? (SHOW WORK)

a. 26×25×24×10×9
b. 26×26×26×10×10
c. 3×2×10×9
d. 3×3×3×10×10

Answer 1

The number of unique IDs possible at the zoo with 3 non-repeating letters followed by 2 non-repeating numbers is 26×25×24×10×9.

Step-by-step explanation:

To calculate the number of unique IDs possible at the zoo with 3 letters followed by 2 numbers where neither numbers nor letters can repeat, we use the counting principle. For the first letter, there are 26 possibilities (A-Z). For the second letter, since we cannot repeat the first letter, we have 25 possibilities. For the third letter, we now have 24 possibilities since two letters have already been used. For the first number, we have 10 possibilities (0-9), and for the second number, we have 9 possibilities since one number has already been chosen. Therefore, the total number of unique IDs is the product of these possibilities: 26×25×24×10×9.