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 of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is

How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels

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

In how many ways a team of $11$ players can be formed out of $25$ players, if $6$ out of them are always to be included and $5$ are always to be excluded

$^n{C_r}{ + ^n}{C_{r - 1}}$ is equal to

Words of length $10$ are formed using the letters, $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated ; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9 x}=$