Question

the set of all three digit numbers, sum of whose digits is less than 3

Answer 1

Answer:

1+1+1=4

so 1 is answer

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Answer 2

Answer:

There are two cases to the answer.

CASE 1: ALL DIGITS ARE EVEN

Even + Even + Even = EVEN

Now, the hundred’s digit can be selected in 4 ways (2 or 4 or 6 or 8). But the ten’s and unit’s place digits can be selected in 5 ways each (0 or 2 or 4 or 6 or 8).

So, TOTAL NUMBERS =4×5×5=100

CASE 2: TWO DIGITS ARE ODD AND ONE DIGIT IS EVEN

Odd + Odd + Even = EVEN

We can select the odd digit in 5 ways. If the even digit comes at the hundred’s place, then we will have 4×5×5=100 numbers

If an odd digit occurs at hundred’s place, then we will have 5×5×5=125 numbers. But again, the arrangement may be Odd-Odd-Even or Odd-Even-Odd. So, 125×2=250 numbers.

So, TOTAL NUMBERS =100+250=350

Thus, the total number of 3-digit numbers sum of whose digits is even = 100+350=450 (Answer)