Tag: exponent of a prime in n!

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 :

Exponent of $4$ in $80\ !$ is

If $^{n}P _{5}=9 \times ^{n-1}P _{4}$, then the value of $n$ is 

In the word $ENGINEERIGNG if all $Es$ are not together and $Ns$ come together then number of permutations is

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 $3.^{n _{1}-n _{2}}P _{2}=^{n _{1}+n _{2}}P _{2}=90$, then the ordered $(n _{1},n _{2})$ is:

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: