Permutations

There are four balls of four different colors. Two balls are taken at a time and arranged in a definite order. For example, if a white and red balls are taken, one definite arrangement is white first, red second, and another arrangement is red first, white second. How many such arrangements are possible?

How many $4$ digit numbers can be formed without repeating any digit from the following digits: $1,2,3,4 \& 6$ ?

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

In how many ways can $6$ distinct books be arranged in a bookshelf?

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

How many permutations are there if the letters PNRCSE are taken six at a time?

What is the number of permutations of the letters in the word BANANA?

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

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

$a,b,c$ 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

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 $2,3,4,5,6,7$

In how many ways can $5$ girls and $6$ boys be arranged in a row so that all the four girls are together?

In how many ways can $7$ people be arranged in a row?

How many $3$ letter words with or without meaning can be formed out of the letters of the word 'SWING' when repetition of letters is not allowed?

In a group of $6$ boys and $5$ girls, $5$ students have to be selected. In how many ways it can be done so that at least $2$ boys are included

In how many ways $5$ Americans and $5$ Indians be seated along a circular table, so that they are seated in alternative positions

In how many ways $4$ Indians, $5$ Africans and $7$ Japanese be seated in row so that all person of same nationality sits together