CEMC Banner

Problem of the Week
Problem C

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:

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.