If $^n{C_r} = {\,^n}{C_{r - 1}}$ and $^n{P_r}{ = ^n}{P_{r + 1}}$, then the value of $n$ is
If $^n{C_r} = {\,^n}{C_{r - 1}}$ and $^n{P_r}{ = ^n}{P_{r + 1}}$, then the value of $n$ is
- A
$3$
- B
$4$
- C
$2$
- D
$5$
Similar Questions
The least value of a natural number $n$ such that $\left(\frac{n-1}{5}\right)+\left(\frac{n-1}{6}\right) < \left(\frac{n}{7}\right)$, where $\left(\frac{n}{r}\right)=\frac{n !}{(n-r) ! r !}, i$
The least value of a natural number $n$ such that $\left(\frac{n-1}{5}\right)+\left(\frac{n-1}{6}\right) < \left(\frac{n}{7}\right)$, where $\left(\frac{n}{r}\right)=\frac{n !}{(n-r) ! r !}, i$
- [KVPY 2017]
In a touring cricket team there are $16$ players in all including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players from these, can be chosen, so as to include three bowlers and one wicket-keeper
In a touring cricket team there are $16$ players in all including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players from these, can be chosen, so as to include three bowlers and one wicket-keeper
On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is
On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is
Find the number of ways in which two Americans, two British, One Chinese, One Dutch and one Egyptian can sit on a round table so that person of the same nationality are separated?
Find the number of ways in which two Americans, two British, One Chinese, One Dutch and one Egyptian can sit on a round table so that person of the same nationality are separated?
Value of $r$ for which $^{15}{C_{r + 3}} = {\,^{15}}{C_{2r - 6}}$ is
Value of $r$ for which $^{15}{C_{r + 3}} = {\,^{15}}{C_{2r - 6}}$ is