Combination Lock The typical combination lock uses three numbe...

Question

Combination Lock The typical combination lock uses three numbers, each between 0 and 49. Opening the lock requires entry of the three numbers in the correct order. Is the name “combination” lock appropriate? Why or why not?

Accepted Answer

Welcome back, everyone. A company requires employees to create a 4 digit passcode using the digits 0 through 9. The same digit can be repeated and the digits must be entered in a specific order to unlock the system. Is it appropriate to call this a combination code? Why or why not? For this problem, let's begin by distinguishing between combinations and permutations. So let's recall that combinations. Those are the arrangements in which the order. Does not matter. Simply speaking, let's suppose that we form a code which is 1250, right? So, A combination that is equivalent to this set of numbers could be, let's say, 0521 going backwards, right? 0521. Because the order does not matter now for permutations. This is where the order matters. Right? So essentially we can say that. 1250 would not be the same as 0521. Those would be two different arrangements, right? Essentially, we can use the same example and say that those would not be equivalent. And now what we're going to do is understand that in this problem, the digits must be entered in a specific order, right? So, we have A permutation. Instead Of A Combination Right? In practice, if we think about the context of this problem, and if we suppose that the code is 1250, then entering 0521 will essentially not lead. To unlocking the system, right? Because those are not the same codes in the context of permutations. Therefore, we can say that the answer to this problem is no. Because The ditches. Must be. Entered In a specific order. Which is our final answer to this problem. Let's label it and conclude the video. Thank you for watching.

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