Counting methods question
How many 4 digit positive integers can be formed without using either ‘3’ or ‘5’?
Correct Answer : Choice A. 3584
We can count the number of such numbers if we can determine the options available for each of the four digits of the 4-digit number starting with the left most (thousands place).
The left most digit (thousands place) cannot be a 0. It can neither be 3 nor 5. So, the left most digit can be anyone of the other 7 digits.
The second digit from the left (hundreds place) cannot be 3 or 5. So, it can be any of the other 8 digits.
The third digit from the left (tens) place cannot be 3 or 5. So, the tens place also has 8 options.
And finally, the units place, the rightmost digit, cannot be 3 or 5. So, the units place also has 8 options.
Therefore, the number of 4 digit positive integers that can be formed without using either 3 or 5 = 7*8*8*8 = 3584.
Choice A is the correct answer