vinay1983 wrote:I presume this will be easy to most of the "solving" people here
How many 4-digit positive integers do not contain the digit 3 or 6?
A. 2401
B. 3584
C. 4096
D. 5040
E. 7200
Take the task of building 4-digit positive integers and break it into stages.
Stage 1: Choose a thousands digit
This can be 1,2,4,5,7,8,or 9, so we can complete stage 1 in
7 ways
Stage 2: Choose a hundreds digit
This can be 0,1,2,4,5,7,8,or 9, so we can complete stage 2 in
8 ways
Stage 3: Choose a tens digit
This can be 0,1,2,4,5,7,8,or 9, so we can complete stage 3 in
8 ways
Stage 4: Choose a units digit
This can be 0,1,2,4,5,7,8,or 9, so we can complete stage 4 in
8 ways
By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus build a 4-digit positive integer) in
(7)(8)(8)(8) ways
IMPORTANT: we don't really need to calculate the product (7)(8)(8)(8)
We can just recognize that the units digit will be 4. That is (7)(8)(8)(8) = ---
4
Since answer choice
B, is the only one with units digit
4, it must be correct.
Cheers,
Brent
Aside: For more information about the FCP, watch our free video:
https://www.gmatprepnow.com/module/gmat-counting?id=775
