The digits 1, 2, 3, 4 can be arranged to form twenty-four different four digit numbers. If these twenty-four numbers are then listed from smallest to largest, in what position is 3142 ?
(A) 13 th
(B) 14th
(C) 15 th
(D) 16 th
(E) 17 th
Solution

The first twelve numbers in the list begin with either the digit 1 or 2 . The next six begin with the digit 3. In order, these six numbers are 3124, 3142, 3214, 3241, 3412, 3421.

We see that the number 3142 is in the fourteenth position.