How many arrangements of the letters of the word $SALOON$ are there,such that the two $O$'s do not come together?

The number of arrangements of the letters of the word $INDEPENDENCE$ in which all the vowels always occur together is

Out of $10$ persons,$A, B$,and $C$ are to speak at a function. If $A$ wants to speak before $B$ and $B$ wants to speak before $C$,in how many ways can they speak?

If a man and his wife enter a bus in which five seats are vacant,then the number of different ways in which they can be seated is

The number of five-digit numbers divisible by $5$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ without repetition is

$5$ men and $4$ women are seated in a row. If the number of arrangements in which one particular man and one particular woman are together is $\alpha$ and the number of arrangements in which those two are not together is $\beta$,then $\alpha: \beta=$