(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.