Let S be the set of all words formed by arranging all the letters of the word GARDEN. From S, one word is selected at random. The probability that the selected word will NOT have vowels (A, E) in alphabetical order is:
Solutions · 1
Official solution
Total arrangements of GARDEN =6!. In exactly half of these, A comes before E (alphabetical order), and in the other half E comes before A (by symmetry).
\[P(\text{not in order}) = 1-\frac12=\frac12\]