An Anthropologist discovers an isolated tribe whose written alphabet
contains only 6 letters (A,B,C,D,E,F). The tribe has a taboo against
using the same letter twice in the same word.It's never done. If each
different sequence of letters constitutes a different word in the
language, what is the maximum number of six-letter words that the
language can employ?

The answer is 720.

You can think of it in this way:

The first letter of a word can be any of the six letters that exist in
the tribe's alphabet. The second letter can be any of the remaining 5
letters. The third letter can be any of 4, and so forth. So the number
of six-letter words in which no letter is repeated is 6! (6
factorial), which is 6 * 5 * 4 * 3 * 2 * 1, or 720.

I hope this helps. If anything is unclear, please request
clarification; I'll gladly offer further assistance before you rate my
answer.

Best regards,
pinkfreud