All valid 5 -digit numbers are formed using the digits 0, 1, 2, 3, and 4 without repetition. If these numbers are arranged in increasing order, what is the position of the number 32014 ?

Step-by-step solution

A valid 5 -digit number cannot have 0 as its leading digit. Number of 5 -digit numbers starting with 1 : 4! = 24 Number of 5 -digit numbers starting with 2 : 4! = 24 For numbers starting with 3 , we must consider the next digits in increasing order: Number of numbers starting with 30 : 3! = 6 Number of numbers starting with 31 : 3! = 6 The next numbers will start with 32 . The remaining available digits are 0, 1, 4 . Arranging these in increasing order gives the smallest number starting with 32 , which is 32014 . T