Name: Andrene

Who is asking: Student

Level: Secondary

Question:

i am really in college but i did this in high school. i am having problem with a question. how many different account numbers are possible if the account numbers consist of a letter of the alphabet, followed by five numerical digits, and followed by another letter.

Hi Andrene,
The account numbers look like

ApqrstB
Where A and B are any of the 26 letters from the alphabet and p, q, r, s and t are any of the 10 digits. You didn't give any restrictions so I am assuming that letters and digits can be used more than once. That is A12321A is a valid account number as is O00000O.
To count the number of account numbers think about constructing **all** of them. To start you have 26 choices for the beginning letter. Next, to each such one character account number you can append any of the 10 digits to put in the second place. Hence each of the 26, one character account numbers can be turned into 10, two character account numbers. Thus for the first two places you have 26x10 = 260 choices.

Now that you have the 260 possible two character account numbers in front of you, to each you can append any of the 10 digits as a third character. This will give 260x10 = 2600 three character account numbers.

The pattern is now clear. In total you have

26x10x10x10x10x10x26 = 67 600 000
possible account numbers.
Penny