Problemas
A combination lock uses three numbers between 1 and 95 with repetition, and they must be selected in the correct sequence? Is the name of "combination lock " appropriate? Why or why not? Choose the correct answer below. A. Yes, because the combinations rule would be used to determine the total number of combinations. B. No, because the permutations rule would be used to determine the total number of combinations. C. No, because the multiplication counting rule would be used to determine the total number of combinations. D. No, because factorials would be used to determine the total number of combinations.
Roztwór
Alfonso
veterano · Tutor durante 10 años
4.4
(216 Votos)
Respuesta
The term "combination lock" is somewhat misleading in this context because the order of numbers matters, which aligns more with permutations rather than combinations. In a true combination scenario, the order does not matter, but for a lock, it does.Let's analyze the options:A. Yes, because the combinations rule would be used to determine the total number of combinations.- This is incorrect because combinations do not consider the order, while the lock requires a specific sequence.B. No, because the permutations rule would be used to determine the total number of combinations.- This is partially correct, as permutations consider order, but since repetition is allowed and each position can have any of the 95 numbers, it's more about counting possibilities rather than strict permutations.C. No, because the multiplication counting rule would be used to determine the total number of combinations.- This is the most accurate choice. Since each of the three positions on the lock can independently be any of the 95 numbers, you use the multiplication principle:
.D. No, because factorials would be used to determine the total number of combinations.- This is incorrect because factorials are typically used in permutations without repetition.Therefore, the correct answer is:C. No, because the multiplication counting rule would be used to determine the total number of combinations.