Question

A computer company uses 6 characters to create their serial number identification for products. the first 3 characters are any single digit number but no character can repeat in those first 3 characters. the next two characters must be a letter and those two letters cannot be the same. the last space can be any number or letter without any restriction. how many unique serial numbers are possible?

a. 11,232,000
b. 24,336,000
c. 15,912,000
d. 16,848,000

Answer 1

d. 16,848,000.

Explanation:

First 3 characters is the number of permutations of 3 numbers from 10

= 10P3 = 10! / (10-3)! = 720 possible ways.

The next 2 characters are letters so the possible permutations are 26P2

= 26! / (26-2)! = 650 ways.

The last character can be any one of 10 + 26 = 36 characters.

So the answer is 720*650*36

= 16,848,000.