Discussion
Let us consider the letters from a through h, and all 5 letters are made using these letters. (words are just strings of letters). How many of these words contain no repeated letters ?
Answer: A
The number of five-letter words with no repeated letter is 6720.
There are 8 letters, a to h. With no repetition, the first position has 8 choices, the next 7, then 6, 5 and 4: these are permutations of 8 objects taken 5 at a time.
\[ P(8, 5) = 8 \times 7 \times 6 \times 5 \times 4 = 6720 \]
6072, 7260 and 7630 are rearrangements of the digits of the right answer, a common trap. Allowing repetition would give \(8^{5} = 32768\), which is not offered.
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