# Problem of the Week Problem C CADET

We can take any word and rearrange all the letters to get another “word”. These new “words” may be nonsensical. For example, you can rearrange the letters in $$MATH$$ to get $$MTHA$$. Geordie wants to rearrange all the letters in the word $$CADET$$. However, he uses the following rules:

• the letters $$A$$ and $$D$$ must be beside each other, and

• the letters $$E$$ and $$T$$ must be beside each other.

How many different arrangements of the word $$CADET$$ can Geordie make if he follows these rules?

Note: $$ADCET$$ and $$ADTEC$$ are acceptable words, while $$ADTCE$$ is not.