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Counting methods question

How many 4 digit positive integers can be formed without using either '3' or '5'?

a. 3584

b. 5416

c. 6416

d. 4096

e. 4904

Correct Answer : Choice A. 3584

Explanatory Answer

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
Labels: SAT counting methods, SAT Number Properties, SAT permutation combination