In an election there are $8$ candidates, out of which $5$ are to be choosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, then in how many ways can a voter vote
$216$
$114$
$218$
None of these
If ${ }^{2n } C _3:{ }^{n } C _3=10: 1$, then the ratio $\left(n^2+3 n\right):\left(n^2-3 n+4\right)$ is
If $^n{C_{12}} = {\,^n}{C_6}$, then $^n{C_2} = $
The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets themselves such that they get consecutive blocks of $5, 3 $ and $2$ tickets is
In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is
A company has $10$ employes. The company has decided to form a team including atleast three employes and also excluding atleast three employes. Then the number of ways of forming the team is