Permutations when All the Objects are Not Distinct Objects

The number of seven digit integers, with sum of the digits equal to $10$ and formed by using the digit $1,2$ and $3$ only, is

The letters of the word "GOPAL" are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary, then the rank of the word "GOPAL" is

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

Find the rank of the word '$\mathrm{POST}$' in the dictionary.

There are $m$ books in black cover and $n$ books in blue cover, and all books are different. The number of ways these $\left(m+n\right)$ books can be arranged on a shelf so that all the book in black cover are put side by side is

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 

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

Consider the word $W=MISSISSIPPI$, Number of ways in which the letters of the word $W$ can be arranged if at least one vowel is separated from rest of the vowels:

The number of sequences of length five by using $0$ and $1$ as terms which contains at least two consecutive $0\text{'}$s are :

The number of $5$ letter words formed with the letters of the word $\mathrm{CALCULUS}$ is divisible by:

Letters of word $\mathrm{INTEGRATION}$ are arranged in all possible manners, then number of ways of arrangements such that :

How many different nine digit numbers can be formed from the number $223355888$ by rearranging its digits so that the odd digits occupy even positions?

Consider the letters of the word 'INCURSION'. Number of arrangements of all letters in which vowels are in alphabetical order, is

Out of 5 digits 0, 3, 3, 4, 5 five digit numbers are formed. If one number is selected at random out of them. The probability that it is divisible by 5 is

If the letters of the word $\mathrm{LATE}$ be permuted and the words so formed be arranged as in a dictionary. Then the rank of $\mathrm{LATE}$ is -

How many different arrangements can be made out of the letters in the expansion $A^2{B}^3{C}^4,$ when written in full?

A dictionary is printed consisting of 7 lettered words only that can be made with the letters of word CRICKET. If words are printed in the alphabetic order as in the dictionary then the number of words before the word CRICKET, is -

All the $7$ digits numbers containing each of the $1,2,3,4,5,6,7$ exactly once and not divisible by $5$ are arranged in increasing order. Find ${2015}^{th}$ number in this list?

In how many shortest ways, can we reach from the point $(1, 2, 3)$ to the point $(4, 5, 4)$ in space where the movement is possible only among the $x$-axis, $y$-axis and $z$-axis or parallel to them and change of axis is permitted only at integral points?