The sum of all $4$ digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

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

How many numbers can be formed using the digits $3, 4, 5, 6, 7, 8$ that lie between $3000$ and $4000$ and are divisible by $5$,given that repetition of digits is not allowed?

In how many ways can a group of $5$ men and $2$ women be made out of a total of $7$ men and $3$ women?

$\binom{n}{n-r} + \binom{n}{r+1}$,whenever $0 \le r \le n-1$,is equal to

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