#Numbers-3

When the natural numbers 1,2,3,4,5,.......,500 then the digit 3 is used n times in this way. The value of n is-
(a)100
(b)200
(c)300
(d)400

SOLUTION:-

  We have 3 places where 3 can come, unit digit, tens digit and hundred digit.
       _   _    _

Now, if we fix 3 at unit digit place,

   _  _  3
At hundred digit place, there can be a total of 5 numbers(0,1,2,3,4) and at tens digit place there can be any of the 10 numbers(0-9)
Total ways = 5*10 = 50------(1)

Similarly when we fix 3 at tens digit place,

 _  3  _
 Again we will have 50 numbers (5*10)------(2)

Similarly fixing 3 at hundred digit place,

3  _  _

Now we will have 10*10 = 100 ----------(3)

Adding these 3 equations we get, 50+50+100 = 200 times ANS

## Counting in such manner had worked because we have to count the number of times 3 appeared, fixing 3 at the unit place will also give 333, fixing 3 at tens place will also give 333 and we will also get 333 when we fix 3 at hundred digits place. We have counted 333 three times which is same as counting number of 3 that will occur in 333.






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