Amit M Agarwal Solutions for Chapter: Permutation and Combination, Exercise 3: Work Book Exercise 6.3

If ${}^{15}P_r={}^{14}P_8+8·{}^{14}P_7,$ then $r$ is equal to

Which of the following is incorrect ?

If ${}^{n+2}C_8:{}^{n-2}P_4=57:16$, then the value of $n$ is:

The exponent of $7$ in ${}^{100}\mathrm{C}_{50}$ is

If ${}^{n-1}C_r=\left(k^2-3\right){}^{n}C_{r+1}$, then $k$ belongs to

If $n$ is even and ${}^{n}C_0<{}^{n}C_1<{}^{n}C_2<\dots <{}^{n}C_r$$>{}^{n}C_{r+1}>{}^{n}C_{r+2}>\dots >{}^{n}C_n,$ then $r$ is equal to

The number of positive integers satisfying the inequality ${}^{n+1}C_{n-2}-{}^{n+1}C_{n-1}\le 100$ are