# Tackling Forbidden Choices in GMAT Combinations Questions

Combinations questions can be hard enough, but when they include “forbidden choices,” things become even more difficult. However, rest assured, there is an easy way.

Consider the following question from The Economist GMAT Tutor:

How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

A) 20

B) 50

C) 225

D) 300

E) 320

The method is to calculate the total number of combinations, without considering the forbidden choice. Then, calculate the number of combinations that **include** the forbidden choice. Finally, subtract the number of forbidden choices from the total number of combinations to arrive at the final answer.

To calculate the total number of combinations, consider each digit individually:

- First digit: There are 4 possibilities: 2, 4, 6, and 8
- Second digit: There are 5 possibilities: 1, 3, 5, 7, and 9
- Third digit: There are 4 possibilities: 2, 3, 5, and 7
- Fourth digit: There are 4 possibilities: 0, 3, 6, and 9 (It would have been very easy to forget that 0 is divisible by )

Multiply these numbers to calculate the total number of combinations:

Now consider the forbidden choice. The forbidden choice is that the digit 2 is used twice. It cannot be used more than twice, as it can only be used as the first and third digits.

- First digit: There is only one possibility: 2
- Second digit: There are 5 possibilities: 1, 3, 5, 7, and 9
- Third digit: There is only one possibility: 2
- Fourth digit: There are 4 possibilities: 0, 3, 6, and 9

Multiply these numbers to calculate the total number of forbidden choices:

Subtract the forbidden choices from the total to calculate the number of allowable combinations:

The key to such questions involving a condition for which there would be too many possibilities to count is therefore to calculate the number of forbidden choices and subtract these from the total. This is usually faster than trying to calculate the number of allowable combinations directly.

*This post appeared first on the **Economist GMAT Tutor** blog.*