How many 3-digit positive integers are odd and do not contain the digit 5 ?

Solution:

We have to find the number of 3-digit positive integers that are odd and do not contain the digit 5.

Odd numbers in 

Unit digit = 1, 3, 7, 9

Number of digits = 4

Tenth digit = 0, 1, 2, 3, 4, 6, 7, 8, 9

Number of digits = 9

100th digit = 0, 1, 2, 3, 4, 6, 7, 8, 9

Number of digit = 9

So, the possible ways = 4 × 9 × 9

= 4 × 81

= 324

Excess 3 digit integer = 4 × 9 = 36

So, 3-digit positive integers = 324 - 36 = 288.

Therefore, there are 288 3-digit positive integers.

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How many 3-digit positive integers are odd and do not contain the digit 5 ?

Summary:

There are 288 3-digit positive integers that are odd and do not contain the digit 5.