A combination lock uses three numbers between 1 and 46 with repetition, and they must be selected in the correct sequence. Is t

Question

4 years ago

15

A combination lock uses three numbers between 1 and 46 with repetition, and they must be selected in the correct sequence. Is t

he name of "combination lock" appropriate? Why or why not? Choose the correct answer below. A. No, because the multiplication counting rule would be used to determine the total number of combinations. B. Yes, because the combinations rule would be used to determine the total number of combinations. C. No, because factorials would be used to determine the total number of combinations. D. No, because the permutations rule would be used to determine the total number of combinations.

Mathematics

1 answer:

vladimir2022 [97] · Answer 1 · 2022-01-15T08:19:05+03:00

The correct answer is D. No because the permutations rule would be used to determine the total number of combinations.

Explanation:

The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) = $\frac{n!}{(n-r) !}$ ; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.