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

There are $12$ members in a group. In how many ways can a team of $6$ members be selected such that a particular member is always included?

How many words can be formed using the letters of the word $COMMITTEE$?

$4$ buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by a different bus,then the total number of possible ways is:

How many words can be formed out of the letters of the word '$EDUCATION$' such that vowels occupy the odd positions?

In how many different ways can the letters of the word '$BANKING$' be arranged so that the vowels always come together?