Question

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 ADT EC are acceptable words, while ADT CE is not.

Answer 1

24 combinations

Explanation:

Using trial and error, you can figure it out. Alternatively, you could do 6 (from there being 6 base arrangements) x 2 (2 arrangements for AD) x 2 (2 arrangements from TE). THis would be 6 x 2 x 2, which is 24.

Answer 2

may be 3

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