The sum of all the $4$-digit numbers formed by taking all the digits from ${2, 3, 5, 7}$ without repetition is:

If all the numbers which are greater than $6000$ and less than $10000$ are formed with the digits $3, 5, 6, 7, 8$ without repetition of the digits,then the difference between the number of odd numbers and the number of even numbers among them is

If $\alpha = ^mC_2$,then $^\alpha C_2$ is equal to

The number of $3$-digit numbers,formed using the digits $2, 3, 4, 5$ and $7$,when the repetition of digits is not allowed,and which are not divisible by $3$,is equal to ..........

In an examination,the maximum marks for each of three subjects is $n$ and that for the fourth subject is $2n$. The number of ways in which a candidate can get $3n$ marks is

The number of ways $5$ boys and $4$ girls can sit in a row so that either all the boys sit together or no two boys sit together,is $......$