In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

At an election,a voter may vote for any number of candidates,not greater than the number to be elected. There are $10$ candidates and $4$ are to be selected. If a voter votes for at least one candidate,then the number of ways in which he can vote is

$8$-digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$. The number of such numbers in which the odd digits do not occupy odd places is:

Number of shortest paths from $HOSTEL$ to $ALLEN$ is equal to (as shown in the given figure):

$A$ person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$,then $n$ equals

There are $4$ notes of Rs. $100$ and $5$ other notes of denominations Rs. $1$,Rs. $2$,Rs. $5$,Rs. $20$,and Rs. $50$. These notes are to be distributed among $3$ children such that each child receives at least one note of Rs. $100$. Find the total number of ways of distribution.