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?

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

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

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 $7$ people be arranged in a row?

There is meeting of $20$ delegates is to be held in a hotel. In how many ways these delegates can be seated along a round table, if three particular delegates always always seat together.

Mr and Mrs Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr Lopez or Mrs Lopez must sit in the driver's seat. How many seating arrangements are possible?

In how many ways can the letters of the word $\mathrm{ABA}-$$\mathrm{CUS}$ be rearranged such that the vowels always appear together?

The number of arrangements that can be formed from the letters of the word "ALLAHABAD":

How many numbers between $1000$ and $10,000$ can be formed with the digits $1,2,3,4,5,6$:

In how many ways $4$ members can occupy $9$ vacant seats in a row:

${}^n{P}_r÷{}^{n-1}{P}_{r-1}$ is

If $4.{}^n{P}_3=5.{{}^{n-1}P}_3$ the value of $n$ is

The number of permutations of $10$ different things taken $4$ at a time in which one particular thing never occurs is _____.

The number of ways in which the letters of the word $\text{'}\mathrm{DOGMATIC}\text{'}$ can be arranged is