Answer:
there are 425 numbers of three digits whose the sum of the digits is even.
Step-by-step explanation:
Option 1:
It is necessary to accomplish one of the next conditions:
(1) all of the digits are even.
(2) exactly 2 of the digits are odd
Then, for the first condition:
4x5x5 = 100 -> this is because the first digit can not be 0.
for the second condition:
(3C1)*5*5*5-1*5*5 =3*125-25=350
where 3C1 is a combination. The 3C1 determines which of the three digits is even, and it is necessary to subtract the numbers under 100 with the other 2 digits odd.
So, there are 450 numbers of three digits whose the sum of the digits is even.
Option 2:
there are 900 three digit number and 5*5*5 =125 has 3 odd numbers and 5*5*5+4*5*5+4*5*5=325 has 1 odd number, so there are 450 numbers of three digits whose the sum of the digitis is odd, so 900-450 whose the sum of the digits is even.
