Question

A national organization plans to issue its members a 4-character ID code. The first character can be any letter other than O. The last 3 characters are to be 3 different digits. If the organization has 25300 members, will they be able to assign each member a different ID code? Explain.

Answer 1

The organization cannot issue a unique 4-character ID code to each of its 25300 members because the total number of possible unique ID codes, which is 18000, is less than the number of members.

Step-by-step explanation:

When determining whether a national organization can issue a unique 4-character ID code to each of its 25300 members, we need to calculate the total number of possible combinations. For the first character, there are 25 possible letters (all the letters of the alphabet except 'O').

For the following three characters, which are to be 3 different digits, we have 10 digits to choose from (0-9), but since we need three different digits, the choices are reduced for each subsequent character (10 options for the first digit, 9 for the second, and 8 for the third).

Thus, the total number of possible unique ID codes is given by the product of these possibilities:

25 (letters) × 10 (first digit) × 9 (second digit) × 8 (third digit) = 25 × 720 = 18000

After performing this calculation, it's clear that the total number of possible unique ID codes (18000) is less than the number of organizational members (25300). Therefore, the organization will not be able to assign a different ID code to each member based on the described constraints.