The number of words that can be formed by using the letter of the word "MATHEMATICS", taken all at a time is

Let $P _m$ stand for $^m P _m$, then,
$1 + P _1 + 2P _2 + 3 P _3 + ... + n.P _n$ is equal to 

The given relation is  $1.P(1,)+2.P(2,2)+3.P(3,3)+......+n.P(n,n)=P)(n+1,n+1)-3$.

If $^{ 56 }{ { P } _{ r+6 } }:^{ 54 }{ { P } _{ r+3 }}=30800$, then $r$ is

In how many ways unique can arrange the  letters  in the word "SUCCESSFUL" 

The given relation is  $1.P(1,1)+2.P(2,2)+3.P(3,3)++n.P(n,n)=P(n+1,n+1)-3$.

How many $4$-letter words, with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

If $^{10}P _r\,= 5040$, then find the value of $r$.

If $ {^n}P _r $ $=$ 5040, then $(n, r)$ $= $

If the last four letters of the word 'CONCENTRATION' are written in reverse order followed by next two in the reverse order and next three in the reverse order and then followed by the first four in the reverse order counting from the end which letter would be eighth in the new arrangement? 

If $ {^1}{^2}P _r  =$ 1320, then r $=$

How many words, with meaning or without meaning, can be formed by using the letters of the word $'MISSISSIPPI'$

If $n$ books can be arranged in a linear shelf in $5040$ different ways then the value of $n$ is

If $ ^nP _{100} = ^nP _{99} $, then $n$ is equal to

How many numbers can be formed by using all the given digits $1,2,8,9,3,5$ when repetition is not allowed

How many words can be formed by taking $4$ letters at a time of the letters of word $MATHEMATICS$ 

There are $20$ persons among whom are two brothers. The number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers, is

The number of permutations of $n$ distinct objects taken $r$ together in which include $3$ particular things must occur together

$2^n P _n$ is .equal to

12 normal dice are thrown once. The number of ways in which each of the values 2,3,4,5 and 6 occurs exactly twice is : [1,1, 2,2, 3,3, 4,4, 5,5, 6,6 can come in any order]

If $^{15}{P _{r - 1}}:{\,^{15}}{P _{r - 2}} = 3:4$ then $r=$

Let ${T _n}$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If ${T _{n + 1}} - {T _n} = 10$. then the value of $n$ is 

The number of all possible different arrangements of the word $"BANANA"$ is

If $\displaystyle \overset{n-r}{\underset{k=1}{\sum }}\ ^{n-k}C _r=^{x}C _y$ then-

If ${}^{15}{P _{r - 1}}\,:\,{}^{15}{P _{r - 2}} = 3:4$, then $r =$

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

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:

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 

If $\displaystyle ^{n+5}P _{n+1} = \frac{11\left ( n-1 \right )}{2}.^{n+3}P _n$ then the value of n is

Find the value of $n$ when:

If P(n, n) denotes the number of permutations of n different things taken all at a time then P(n, n) is also identical to

$\displaystyle ^{n}P {n}=$___.

In an examination hall, there are four rows of chairs. Each row has $8$ chairs one behind the other. There are two classes sitting for the examination with $16$ students in each class. It is desired that in each row all students belong to the same class and that no two adjacent rows are allotted to the same class. In how many ways can these $32$ students be seated?

$\displaystyle ^{5}P {4}=$___.

'$X$' completes a job in $2$ days and '$Y$' completes it in $3$ days and '$Z$' takes $4$ days to complete it. If they work together and get Rs. $3,900$ for the job, then how much amount does '$Y$' get?

In how many ways the letters of the word $'LEADER '$ can be arranged?

Find the number of words, with meaning or without meaning, that can be formed by arranging the letters of the word $'EIGHT'$ in all possible ways 

Find the number of ways in which the letters of the word $'AEROPLANE'$ can be arranged such that the vowels are always together.

In how many ways can you partition $6$ into ordered summands? (For example, $3$ can be partitioned in $3$ ways as : $1 + 2, \,2 + 1, \,1 + 1 + 1$)

If $^{56}P _{r+6} : ^{54}P _{r+3} = 30800:1$ find $r$.

A bag contains  $4$ red,  $3$ black, and  $2$ white balls. If  $2$  balls are selected at random, the probability of selecting atleast one white ball is

Which of the following is true ?

If $\displaystyle \frac{^{n}P _{r-1}}{a}=\frac{^{n}P _{r}}{b}=\frac{^{n}P _{r+1}}{c}$,then which of the following holds good