Question

1. a special safe lets you choose from 7 symbols for a 4 - symbol - long pass code. you may enter a symbol any number of times. how many potential pass codes are there? 35 16384 840 2401

Explanation:

Step1: Identify the problem type

This is a permutation with repetition problem. For each position in the 4 - symbol passcode, we have 7 choices (since we can reuse symbols).

Step2: Apply the formula for permutations with repetition

The formula for the number of permutations of \(n\) objects taken \(r\) at a time with repetition is \(n^r\), where \(n = 7\) (number of symbols) and \(r=4\) (length of the passcode).
So we calculate \(7^4\).

Step3: Calculate \(7^4\)

\(7^4=7\times7\times7\times7 = 2401\).

Answer:

2401