The UKMT Senior Challenge is a national competition. We have 15 mathematicians across the campus who have chosen to take part in the event.
They have to answer a series of multiple choice questions (with penalties for incorrect answers, or guesses!) to be in with a chance of competing against other students nationally at the Senior Kangaroo or the British Mathematical Olympiad.
The questions that students face are intended to stretch their problem solving skills beyond what they might be expected to know in the classroom.
Aaron has to choose a three digit code for his bike lock. The digits can be chosen from 1 to 9. To help him remember them, Aaron chooses three different digits in increasing order, for example 278.
How many such codes can be chosen?