$^n{C_r}\,{ \div ^n}{C_{r - 1}} = $
$\frac{{n - r}}{r}$
$\frac{{n + r - 1}}{r}$
$\frac{{n - r + 1}}{r}$
$\frac{{n - r - 1}}{r}$
If $^n{C_r} = {\,^n}{C_{r - 1}}$ and $^n{P_r}{ = ^n}{P_{r + 1}}$, then the value of $n$ is
There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed
How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number
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
Let $A_1,A_2,........A_{11}$ are players in a team with their T-shirts numbered $1,2,.....11$. Hundred gold coins were won by the team in the final match of the series. These coins is to be distributed among the players such that each player gets atleast one coin more than the number on his T-shirt but captain and vice captain get atleast $5$ and $3$ coins respectively more than the number on their respective T-shirts, then in how many different ways these coins can be distributed ?