2024 MI H1 Q9

1. Find the number of different arrangements of the \(9\) letters of the word SUNFLOWER in which
   1. there is no restriction,[1]
   2. the letters are not in alphabetical order,[1]
   3. each of the \(3\) vowels (E, O and U) is not adjacent to another vowel.[2]

\(5\) letters are now selected from the \(9\) letters of the word SUNFLOWER at random. Once a letter has been selected, it cannot be selected again.

2. Find the probability that the selection contains more consonants than vowels.[4]