Skip to main content
OlympiadHQ

Browse · harp

Print

imc

counting and probability intermediate

Problem

How many even integers are there between and whose digits are all different and come from the set ?
(A)
(B)
(C)
(D)
Solution
We split up into cases of the hundreds digits being or . If the hundred digits is , then the units digits must be in order for the number to be even and then there are remaining choices () for the tens digit, giving possibilities. Similarly, there are possibilities for the case, giving a total of possibilities.
Final answer
A