Question

How many integers between 500 and 1000 contain both the digits 3 and 4?

Answer 1

$\huge \fbox \pink{Answer}$

The required numbers are greater than 500 but less than 1000 and all are three digit numbers.

So the hundreds digit can be filled by any one of 5, 6 or 9.

The hundreds digit can be filled by any one of the six numbers 0,1,2,5,6 and 9.

Similarly the ones digit.

So the required number of three digit numbers

= 3×6×6 = 108.

Answer 2

The required numbers are greater than 500 but less than 1000 and all are three digit numbers.

The required numbers are greater than 500 but less than 1000 and all are three digit numbers.So the hundreds digit can be filled by any one of 5, 6 or 9.

The required numbers are greater than 500 but less than 1000 and all are three digit numbers.So the hundreds digit can be filled by any one of 5, 6 or 9.The hundreds digit can be filled by any one of the six numbers 0,1,2,5,6 and 9.

The required numbers are greater than 500 but less than 1000 and all are three digit numbers.So the hundreds digit can be filled by any one of 5, 6 or 9.The hundreds digit can be filled by any one of the six numbers 0,1,2,5,6 and 9.Similarly the ones digit.

The required numbers are greater than 500 but less than 1000 and all are three digit numbers.So the hundreds digit can be filled by any one of 5, 6 or 9.The hundreds digit can be filled by any one of the six numbers 0,1,2,5,6 and 9.Similarly the ones digit.So the required number of three digit numbers

The required numbers are greater than 500 but less than 1000 and all are three digit numbers.So the hundreds digit can be filled by any one of 5, 6 or 9.The hundreds digit can be filled by any one of the six numbers 0,1,2,5,6 and 9.Similarly the ones digit.So the required number of three digit numbers= 3×6×6 = 108.