Permutation

In how many ways, six boys and six girls be seated in a row alternatively ?

In how many ways, six boys and three girls be seated in a row so that the three girls do not sit together?

If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be

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

Consider the word "INDEPENDENCE". The number of words such that all the vowels are together is

During school function for a particular program 4 boys and 3 girls are to be seated in a row wearing colourful dresses. Concerned teachers-in-charges are trying all possible ways of arrangements. Help them answering the following. (i) In how many ways can seated?

Find the number of permutations of the letters of the word $\mathrm{UBUNTU}?$

Number of ways in which all the letters of the word ORTHOGONAL be arranged such that no two O's are together is 

Derivation of ${}^n{P}_r$

Prove that $\frac{n^2!}{{\left(n!\right)}^n}$ is an integer,$n\in N$.

How many numbers more than $10000$ can be made using $1,2,0,2,4?$

$a,b,c$ are three particular speakers among the $10$ speakers of a meeting. The number of ways of arranging all the $10$ speakers on the dias in a row so that all the three speakers $a,b,c$ do not sit together is

$5$ boys $\left(B_1,B_2,B_3,B_4 \text{and} B_5\right)$ and $5$ girls $\left(G_1,G_2,G_3,G_4 \text{and} G_5\right)$ are to be seated around a round table such that boy and girl sit alternately and $B_1$ does not sit beside $G_i\forall i\in \left\{1,2,3,4,5\right\}.$ If the number of such arrangements is $N$, then the sum of digits of $N$ is equal to $?$

In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?

How many numbers greater than $1000000$ can be formed by using the digits $1, 2, 0, 2, 4, 2, 4$?

Find the number of words with or without meaning which can be made using all the letters of the word $\mathrm{AGAIN}$. If these words are written as in a dictionary, what will be the ${50}^{\mathrm{th}}$ word?

How many $4$-digit numbers can be formed by using the digits $1$ to $9$ if repetition of digits is not allowed?

Find the number of permutations of the letters of the word $\mathrm{ALLAHABAD}$.

If ${}^{n}P_4={20}^n{P}_2$ where $P$ denotes the number of permutations, then $n=$ ________

How many number divisible by $5$ of $6$ digit can be made from the digit $2,3,4,5,6,7$