Question

In how many different ways can the letters of the word 'SALOON' be arranged ,
i. if the two o's must not come together ?
ii. if the consonants and vowels must occupy alternate places ?

Answer 1

(i)
there are 5!5! letters spelled "salno" and we put the remaining $o$ in the $4$ space in the word spelling "salono." we need to divide by $2$.
$5!\ast 4/2=240$
(ii)
$6$ ways to orient the consonants, and $3$ ways to orient the vowels (again that double $o$ thing). We could start with a vowel, or we could start with a consonant.
$6\ast 3\ast 2=36$