Question

Everybody at a company is assigned a unique 8 digit id. how many unique ids exist? (note: you should also count the id consisting of all zeros)

Answer 1

If everybody at a company is assigned a unique 8-digit id, then 3628800 unique IDs exist.

What is a unique ID?

• Any document that can be used to prove a person's identity (also known as ID or paper) is considered an identity document.
• It is commonly referred to as an identity card (IC, ID card, citizen card), or passport card when issued in the form of a small, standard credit card.
• Some countries issue formal identity documents, such as national identification cards, which may be required or optional, whereas others may require identity verification via regional identification or informal documents.
• A photo ID is a form of identification that includes a person's photograph.

To find out the number of unique IDs:

• Given, assigned unique id= 9 digits.
• Unique numbers= 1,2,3,4,5,6,7,8,9,0

Then,

• n = 10
• unique number: r = 9 digits

Using formula:

$\begin{aligned}\rightarrow{ }^n P_r=\frac{n !}{n-r !} \\\rightarrow P_9^{10} &=\frac{10 !}{(10-9 !)} \\&=\frac{10 !}{(10-9 !)} \\&=\frac{10 !}{(1 !)} \\&=\frac{10 !}{1} \\&=3628800\end{aligned}$

Therefore, if everybody at a company is assigned a unique 8-digit id, then 3628800 unique IDs exist.

Know more about a unique ID here:

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The correct question is given below:
Everybody at a company is assigned a unique 9-digit ID. How many unique IDs exist? (note: you should also count the id consisting of all zeros)