SOLUTION: How many words can be formed using letter of DEPARTMENT using each letter at most once?

Question 1138935: How many words can be formed using letter of DEPARTMENT using each letter
at most once?
i) If each letter must be used,
ii) If some or all the letters may be omitted.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

            The post is not absolutely clear to be considered as a Math problem.

            Let me explain why.

The given word "DEPARTMENT" has two identical letters "E" and two identical letters "T".


One part of the condition assign me to use each letter at most once.

The other part says "each letter must be used".


Under these instructions, I don't know if I can and if I should use the letter "E" twice.


Same about letter "T".


Also, should I consider permutations of two different instances of "E" between themselves inside a word as giving different words ?

As you, probably, understand, a TRUE MATH problem should not leave a room for such doubts.

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