Tag: combinatorics and mathematical induction

If $^{2n+1}P _{n-1}:^{2n-1}P _n=7:10$, then $^nP _3$ equals

There are m apples and n oranges to be placed in a line such that the two extreme fruits being both oranges. Let P denotes the number of arrangements if the fruits of the same species are different and Q the corresponding figure when the fruits of the same species are alike, then the ratio P/Q has the value equal to :

If $^{2n + 1}P _{n -1} : ^{2n - 1}P _n = 3 : 5$, then n is equal to 

Number of ways in which these $16$ players can be divided into equal groups, such that when the best player is selected from each group, ${P} _{6}$ is one among them, is $(k)\dfrac{12!}{{4!}^{3}}$. The value of $k$ is:

The number of one one functions that can be defined from $A={a,b,c}$ into $B=1,2,3,4,5}$ is

The number of ways in which $8$ different flowers can be strung to form a garland so that $4$ particulars flowers are never separated, is?

If $\displaystyle ^{n}P _{3}:^{n}P _{6}=1:210$, find $n$.

Total number of $6-$digit numbers in which all the odd digits and only odd digits appears, is

Total number of $6-$ digit numbers in which all the odd digits and only odd digits appear, is

The number of many one functions from $A=}1,2,3}$ to $B={a,b,c,d}$ is