SOLUTION: A typical combination lock is opened with the correct sequence of three numbers between o and 39 inclusive. (I) how many different "combinations" are possible if a number can be u

Question 1069677: A typical combination lock is opened with the correct sequence of three numbers between o and 39 inclusive.
(I) how many different "combinations" are possible if a number can be used more than once (like 27-27-27)? *both permutations and combinations require "without replacement" so this isn't either of those.
(II) How many different "combinations" are possible if no number can be repeated?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A fifth-grader approach works:
(I) how many different "combinations" are possible if a number can be used more than once (like 27-27-27)?
There are
possible choices for the first number,
possible choices for the second number, and
possible choices for the third number.
So the total number of possible sequence choices is
.
Maybe your instructor would call that "permutations with replacement."

(II) How many different "combinations" are possible if no number can be repeated?
There are
possible choices for the first number,
possible choices for the second number, and
possible choices for the third number.
So the total number of possible sequences without repeated numbers is
.
Maybe your instructor would call that "permutations without replacement."

Combinations, permutations, replacement are words you are required/expected to use in your class.
You are instructed to identify the "type of problem" and apply the solving procedure prescribed for that "type of problem."
Once your head is filled with someone else's words and problem-solving recipes,
you try to faithfully execute the programs installed in your head.
You search for the imposed words and recipes instead of just thinking about the situation as a human would.
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