Permutations of Security Codes
How many different security codes are possible?
To open the lock, you must enter the correct security code by pressing three buttons in succession. Given the available colors RED, BLUE, GREEN, YELLOW, and ORANGE, how many unique security codes can be generated?
Answer:
The total number of different security codes possible is 125.
The question deals with permutations in mathematics. Given that we have 5 available colors and we need to select 3 in any order with repetition allowed, the total number of security codes possible is determined by the formula 5^3, which equals 125.
Understanding Permutations:
The question is related to the principles of combinatorics, specifically the permutation rule. In mathematics, permutation refers to arranging the members of a set into a specific sequence or order.
In this scenario, there are 5 different colored buttons available, and we need to press 3 buttons in succession to open the security lock. It is important to note that the colors can be repeated in the security code.
By having 5 choices (colors) for each button press and a total of 3 button presses required, the number of possible code combinations can be calculated by multiplying the number of choices for each button press together. In mathematical terms, this is expressed as 5 (possible choices) raised to the power of 3 (number of choices to make) or 5^3.
Therefore, the number of different security codes possible is 5^3, which equals 125 possible unique combinations.