SOLUTION: how many three digit numbers can be formed from the set 0-9 if repetition are allowed and the number must be a).even b).divisible by 5 c).divisible by 10

Algebra.Com
Question 1169499: how many three digit numbers can be formed from the set 0-9 if repetition are allowed and the number must be a).even b).divisible by 5 c).divisible by 10

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
how many three digit numbers can be formed from the set 0-9 if repetition are allowed and the number must be
a)even
--> the 1's digit must be 0, 2, 4, 6 or 8
Units is 1 of 5
Tens is 1 of 10
Hundreds is 1 of 10
---> 5*10*10
========================
b)divisible by 5
---> Units is 5 or 0
Tens is 1 of 10
Hundreds is 1 of 10
---> 2*10*10
======================
c)divisible by 10
---> Units is 0
Tens is 1 of 10
Hundreds is 1 of 10
---> 10*10
===============================
All assuming leading zero is acceptable, eg, 012.
If not, you need to specify that.




Answer by ikleyn(52866)   (Show Source): You can put this solution on YOUR website!
.

            In such problems,  the term  "three digit number"  means,  by default,  the number having  NON-ZERO  leading digit.

            Therefore,


(a)  the last, ones digit, is any of 5 options 0, 2, 4, 6, 8.

     the tens digit is  any from 0 to 9 : 10 options;

     the leading digit: any from 1 to 9 :  9 options.


     Total amount of such numbers is  9*10*5 = 450.


     The same answer you can obtain by different way
         noticing that there are 900 three-digit numbers from 100 to 999,
         and exactly half of them are even numbers.




(b)  If a three-digit number is divisible by 5, its ones digit must be 0 or 5.

     So, the amount of such three-difit numbers is 9*10*2 = 180.


     Again, it is exactly    part of the total 900 three-digit numbers.



(c)  Let me be short in this last case:


     The amount of the three-digit numbers divisible by 10 is exactly    part 
     of the total 900 three-digit numbers, i.e. 90, in total.

Solved.

All questions are answered.


RELATED QUESTIONS

How many three digit numbers can be formed from the set 0-9 if repetition are allowed and (answered by Edwin McCravy)
How many three digit numbers can be formed from the set 0-9 if repetitions are allowed... (answered by Fombitz)
How many 3 digit numbers can be formed from 1,2,3,4,5,6 if a) repition is allowed b)... (answered by swincher4391)
Consider the numbers 2, 3, 5, and 9. If repetition is not allowed, how many three digit... (answered by ewatrrr,stanbon)
consider the number 0, 1 ,3,5,6 how many three digit numbers can be formed a: repetition... (answered by solve_for_x)
How many 3-digit numbers can be formed from the set 0-9 if repetitions are not allowed... (answered by greenestamps,ikleyn)
How many different 5 digit numbers can be formed from the digit 1,2,3,4 and 5 if (i).... (answered by ikleyn)
How many 4 digit numbers can be formed with the 10 digit ie (.0,1,2,3,4,5,6,7,8,9) if... (answered by Edwin McCravy)
If given the digits 1,3,4,6,7,9, how many 4-digit numbers can be formed if the number... (answered by stanbon)