Question

How many 3 digit numbers contain 5 as one of their digits?

• A. 271
• B. 252
• C. 300
• D. 243

Answer 1

The correct option is B

252

Total number of 3 digit numbers = 999-99= 990
Those not having 5 s any of their digits = 8$\times$9$\times$9=648
Those having 5 as one of their digits = 990-648 = 252

Alternate Solution:
This can also be manually counted.
5 can come either in hundreds place or tens place or units place.
In hundreds place: 500 to 599 : 100 numbers.
In tens place: x 5y where y can take values from 0 to 9 and x can take values from 1 to 9 (except 5) = 80 numbers.
In units place: xy5 where y can take values from 0 to 9 (except 5) and x can take values from 1 to 9 (except 5) = 72 numbers.

Total = 100 + 80 + 72 numbers = 252 numbers.