Question

a password contains seven digits, such as 1746678. how many different passwords can be formed?

different passwords can be formed.

Explanation:

Step1: Determine the number of choices for each digit

Each digit in the password can be chosen from 0 - 9, so there are 10 choices for each of the 7 digits.

Step2: Use the multiplication principle

By the multiplication principle of counting, if there are \(n_1\) ways to do the first task, \(n_2\) ways to do the second task, \(\cdots\), \(n_k\) ways to do the \(k\) - th task, then the total number of ways to do all \(k\) tasks together is \(n_1\times n_2\times\cdots\times n_k\). Here \(n_1 = n_2=\cdots=n_7 = 10\), and the total number of passwords \(N=10\times10\times10\times10\times10\times10\times10\).
We can write \(10\times10\times10\times10\times10\times10\times10 = 10^7\)

Answer:

\(10000000\)