Question:If the 6 letters in the word NEEDED are randomly rearranged, what is the probability that the resulting string of letters will not be in alphabetical order?
Permutations with duplicates formula will be needed to determine how many letter combinations are possible.
\(n\) = NEEDED = 6; The word "needed" has a total of 6 objects.
\(n_1\) = E = 3; E is repeated 3 times.
\(n_2\) = D = 2; D is repeated 2 times.
\( \frac{(n!)}{(n_1!)(n_2!)} = \frac{(6!)}{(3!)(2!)}\)
...
Permutations with duplicates formula will be needed to determine how many letter combinations are possible.
\(n\) = NEEDED = 6; The word "needed" has a total of 6 objects.
\(n_1\) = E = 3; E is repeated 3 times.
\(n_2\) = D = 2; D is repeated 2 times.
\( \frac{(n!)}{(n_1!)(n_2!)} = \frac{(6!)}{(3!)(2!)}\)
...
