# The two most misused formulas in GMAT Quant

On the GMAT, the combinations and permutations formulas tend to be challenging for many because they are hard to understand intuitively.

To deal with abstract calculations, many of us rely on memorisation of the combinations and permutations formulas. These formulas are indeed useful, but the problem is that they are often misapplied. These two formulas are:

- The Permutations Formula:
- The Combinations Formula:

To help sort out which formula to use, we’ve created this handy flow-chart, which will help you approach each problem systematically and eliminate any fuzziness in your decision-making:

Anytime you encounter a problem on the GMAT involving arrangements, ask yourself where the problem fits into this flow-chart. If there are multiple sources or if repetition is allowed, neither the combinations nor probability formula can be used; we must fall-back to more general techniques. If all the items, however, come from a single source and involve no repetition, then we can use one of the two formulas. If order matters, then choose the permutations formula; otherwise, choose the combinations formula. To illustrate, let’s analyse a sample problem:

In Wake Forest there are 8 trees. 3 of them have to be cut down during a deforestation process. How many options are there to choose 3 trees?

First, notice that the trees of Wake forest all come from a **single source**: we are choosing 3 trees out of the same source of 8 trees in Wake Forest. We are not, for instance, choosing 3 plants amongst a garden consisting of 4 shrubs, 5 trees, and 6 vines. Instead, we have just a **single source** of items to choose from.

Secondly, notice that **repetition is not allowed**. It would be impossible to cut down the same tree 3 times; the three trees selected must therefore be different trees.

Finally, in this problem, **order does not matter**. The question does not scruple over which tree was cut first, second, and third; so long as the three trees are selected, the order in which they are cut does not matter. So far, we have identified that this problem uses a single source, has no repetition, and ignores order. Using our flow-chart, we quickly identify that this problem can be solved using the combinations formula. Since we are selecting 3 trees out of 8, plug-in n = 8 and k = 3 to get: