SOLUTION: How many four-digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Algebra ->  Permutations -> SOLUTION: How many four-digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8, and 9 if the first digit cannot be 0? Repeated digits are allowed.      Log On


   

Question 1132040: How many four-digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8, and 9 if the first digit cannot be 0? Repeated digits are allowed.
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
It can be calculated and presented by different ways.


The simplest and most straightforward way is to notice that this set of numbers is EXACTLY the set of all 4-digit numbers from 1000 to 9999, 

which consists of  9999 - 999 = 9000 numbers.     ANSWER




Another way is to count them as follows:


    Any of 9 digits from 1 to 9 in the most left position.     9 options

    Any of 10 digits from 0 to 9 in the next position.        10 options.

    ---------------------- " ------------------------         10 options

    ---------------------- " ------------------------         10 options



In all, there are  9*10^3 = 9000 such numbers.    The same answer.

Solved.