My name is Sara, and this is a secondary education question asked by a teacher.
The question is:
A combination lock has three dials numbered 0 - 9. Give a mathematical reason why "combination" is a bad name for this type of lock.
Hi Sara,
We have two answers for you, one from Penny
How many different "combinations" are there? Is this number a combination or a permutation? What is the important difference between combinations and permutations?
Penny
and a second from Chris.
Wrong question! "Combination" is an appropriate name for such a lock.
Look the word up in any dictionary. It's the mathematicians who are at
fault here. "Combination" was the 19th century English word used for
"subset" (before the concept of subset was invented). This use of the word
persists only in mathematics; the current meaning in common English is
different enough to cause confusion. The real question is why do
mathematicians continue to use that obsolete word when counting subsets,
even though they use the word "subset" everywhere else?
Chris