The number of natural numbers,between $212$ and $999$,such that the sum of their digits is $15$,is . . . . . .

There are $(n + 1)$ white and $(n + 1)$ black balls,with each set numbered $1$ to $n + 1$. The number of ways in which the balls can be arranged in a row so that no two adjacent balls are of the same colour is

The number of ways in which we can select three numbers from $1$ to $30$ such that we exclude every selection consisting of all even numbers is

The number of all possible combinations of $4$ letters which are taken from the letters of the word $ACCOMMODATION$ is

The number of ways in which $4$ different things can be distributed to $6$ persons so that no person gets all the things is

Five-digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers. For example,the number $77777$ has serial number $1$. Then the serial number of $35337$ is $.........$.