Permutation

The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently, is

The number of different four letter words can be formed with the words ‘RATE’ is

The value of ${}^{10}P_4$ is 

The number of different four letter words can be formed with the words ‘DATE’ is

The value of ${}^{10}P_3$ is 

If $\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}$, then $x$ is equal to

In how many different ways can the letters of the word ‘INCREASE’ be arranged?

If ${}^n{P}_4=5\left({}^n{P}_3\right),$ then the value of $n$ is equal to

Find the number of ways of arranging the letter of the word $"\mathrm{MATHEMATICS}"$.

Number of ways of arranging letters of the word $\mathrm{MATHEMATICS}$ is 

The sum of four digit even numbers that can be formed with the digits $0, 3, 5, 4$ without repetition is

The number of ways of arranging $8$ boys and $8$ girls in a row so that boys and girls sit alternately is

In how many different ways can the letters of the word $\mathrm{INCREASE}$ be arranged?

If $2\le n\le 500$, then the number of integers such that the highest common factor of $n$ and $350$ is $1$:

The number of ways in which $3$ book can be placed in $4$ racks with at most one book in each rack is:

If $n$ satisfies the relation ${}^{n+5}{P}_{n+1}=\frac{11\left(n-1\right)}{2}{\times }^{n+3}{P}_n$, then number of point of intersection of $n$ straight lines is

The number of ways in which $4$ boys and $4$ girls can sit alternatively in a row if a particular boy and a particular girl are never adjacent to each other, are

Two girls and four boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?

The set $A$ has $4$ elements and the set $B$ has $5$ elements$,$ then the number of injective mappings that can be defined from $A$ to $B$ is

The no. of different signals that can be made by $5$ flags from $8$ flags of different colours is