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.Com
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)   (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.


RELATED QUESTIONS

Four-Digit Number. How many four-digit numbers can be formed using the digits 0, 1, 2, 3, (answered by MathLover1,jilalbenkad)
How many 7-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 if... (answered by hitarth)
How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if... (answered by MathLover1)
How many odd 4 digit numbers can be formed using digits 0 to 9 such that digits cannot... (answered by ewatrrr)
How many 6 digit numbers can be formed using 0, 1, 2, 3, 4, 5, 6, 7, 8 and... (answered by Alan3354)
How many different two-digit numbers can be formed using the digits 1, 3, 4, and 5.... (answered by stanbon)
How many five-digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8,&9 if the... (answered by josmiceli)
How many different four-digit numbers can be formed from the digits 0 through 9 if the... (answered by solver91311)
How many different four digit numbers can be formed from the digits 0 through 9 if the... (answered by josmiceli)