Tag: combinatorics and mathematical induction

The number of arrangements of ${ A } _{ 1 },{ A } _{ 2 },\dots ,{ A } _{ 10 }$ in a line so that  ${ A } _{ 1 }$ is always above than ${ A } _{ 2 }$. Is

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

The number of ways od arranging 9 persons around a circle of there are two other persons between two particular persons is 

The number of 7 digit numbers which can be formed using the digits 1,2,3,2,3,3,4 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 :

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: