## Discussion Forum

### Daily Magic Spell Discussion - January 4, 2017

Daily Magic Spell Discussion - January 4, 2017

For today's discussion, we will discuss about the Daily Magic Spell given on January 4, 2017.

Problem: How many possible rearrangements of $BANANAS$ are there?

Solution: There are $\displaystyle \frac{7!}{3!2!}= 420$ possible rearrangements of $BANANAS$,

Some students may attempt a brute force approach trying to count all possible arrangements of the letters. This is prone to miscounting since there are a lot of rearrangements. Do not try breaking up the problem by looking at specific cases (such as grouping "A's" or "N's")

If one would approach this method, there would be a case when the maximum number of consecutive A's is 1, 2, or 3, and the maximum number of consecutive N's is 1 or 2. This yields 6 total cases to consider.

This will easily become problematic as you would have to try and develop various approaches to tackle this problem per case.

If you have an approach that you would like to share, please let us know!