What proportion of the first 10,000 natural numbers contain a 3

we know that

It is much easier to compute the number of numbers that do not contain a .

In the first numbers do not contain a .

In the first numbers do not contain a . (This is because these numbers are formed by selecting a digit out of

for the first position and another digit out of the same set for the last position and this may be done in

In the first numbers, reasoning as above, there are

numbers that do not contain a .

Now the pattern should be becoming obvious.

In the first numbers there are numbers that do not contain a .

So

In the first numbers there are numbers that do not contain a .

Thus

the ratio of those numbers that do contain a 3 over the total is equal to

therefore

the answer is

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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