Question

At oxnard university, a student id consists of one letter (26 possibilities) followed by eight digits (10 possibilities). (a) how many unique student ids can be created? number of student ids (b) would one letter followed by three digits suffice for a university with 43,000 students? yes no

Answer 1

A. We are given that the combination is 1 letter and 8 digits, so the total number of unique combinations would be the product of each possibilities.

Total unique ID’s = 26 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10

or can also be written as

Total unique ID’s = 26 * 10^8

Solving:

Total unique ID’s = 2.6 x 10^9

B. Let us now calculate the total unique ID’s if there is only 1 letter followed by 3 digits.

Total unique ID’s = 26 * 10^3

Total unique ID’s = 26,000

Since there are 48,000 students and only 26,000 unique ID’s, therefore it is not enough.

NO.