Serial numbers for a product are to be made using 2 letters followed by 4 numbers. If the letters are to be taken from the first 9 letters of the alphabet

Question

Serial numbers for a product are to be made using
2
letters followed by
4
numbers. If the letters are to be taken from the first
9
letters of the alphabet with no repeats and the numbers are taken from the digits
0
through
9
with repeats possible, how many serial numbers can be generated?

Answer 1

Hi,

This problem can be solved using Counting Principle or by Permutation and Counting Principle.

 

__ __ __ __ __ __

 

There are 9 possible letters with no repeats for the first and 8 for the second. However, since repeats are possible for the last four spaces and there are 10 digits from 0 through 9, there are 10 numbers for each of the four spaces. Therefore, 

 

9 · 8 · 10 · 10 · 10 · 10 = 720,000 

 

Second method:

 

₉P₂  · (10 · 10 · 10 · 10) =720,000

 

I think this will help you.

SN