Answer
(sample answer)
When taking r distinct elements at a time from a set of n elements,
if the order of selecting or presenting the r elements matters, we are talking about permutations.
If the order is unimportant, we have combinations.
Say that we are selecting from the set of n=10 digits.
Examples of combinations problems:
- choose 3 "lucky" digits
- make a 4 element subset consisting of these digits.
Examples of permutations problems
- make a 4-digit passcode for your padlock, with no digits repeating.
- select a PIN (personal ID) made of 5 digits, with no digits repeating.
- write all arrangements using all the ten digits.
Work Step by Step
Note: the "no repetition" clause serves the purpose of selecting r distinct elements from the set of n elements.
