Alphabet
Including nonsense words, how many three letter words can be made using the English alphabet if no letters can be repeated in a single “word”?
Expand Hint
There are 26 letters in the English alphabet.
Hint 2
The number of different permutations of "n" distinct objects taken "r" at a time is:
$$$P_{(n,r)}=\frac{n!}{(n-r)!}$$$
The number of different permutations of "n" distinct objects taken "r" at a time is:
$$$P_{(n,r)}=\frac{n!}{(n-r)!}$$$
A permutation is an arrangement or sequence of selections of objects from a single set. Unlike a combination, the order in which elements are selected or arranged is significant. In this problem, there are 26 distinct objects (
$$n=26$$
) to choose from the English alphabet to make a three letter “word” (
$$r=3$$
). Thus,
$$$P_{(26,3)}=\frac{26!}{(26-3)!}=\frac{26!}{23!}=\frac{26\cdot 25 \cdot 24 \cdot 23!}{23!}=15,600$$$
15,600
Time Analysis
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