Permutation and combination practice · Medium

The number of permutations of the letters of the word 'HINDUSTAN' such that neither the pattern 'HIN' nor 'DUS' nor 'TAN' appear, are

If the number of ways of selecting $m$ cards out of unlimited number of cards bearing the number
2, 3, 4 so that they can not be used to write the number 423 is 93. Then $m$ is equal to

5- digit numbers are to be formed using $2,3,5,7,9$ without repeating the digits. If $p$ be the number of such numbers that exceed 20000 and $\mathrm{q}$ be the number of those that lie between 30000 and 90000 , then $p: q$ is :

6 white and 6 black balls are distributed among ten identical urns, so that there is atleast one ball in each urn. Balls are all alike except for the colour and each box can hold any number of balls. The number of different distributions of the balls is:

There are 20 persons among whom two are brothers. The number of ways in which we can arrange them around a circle so that there is exactly one person between the brothers is

The number of ways in which 10 person can sit around a table so that they do not have same neighbor (all at once) in any two arrangements

The range of the function $f(x)={ }^{15-x} P_{x-8}$ is

Let $E=\left[\frac{1}{3}+\frac{1}{50}\right]+\left[\frac{1}{3}+\frac{2}{50}\right]+\left[\frac{1}{3}+\frac{3}{50}\right]+\ldots+50 \text { terms,}$ then the exponent of 2 in $E$! is

$S_n=1 !+2 !+3 !+4 !+\ldots+n !$ cannot be the square of natural number except for $n$, is

The number of non-negative integral solutions of $a+b+c+d=n, n \in N$, is

There are 5 different coloured balls and 5 boxes of the same colour as that of the balls. The number of ways that exactly 2 balls will go to the boxes of their own colour is

In a town the car plate numbers contains only three or four digits, not containing the digit 0. The
maximum number of cars that can be numbered is

A team of four students is to be selected from a total of 12 students. Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only, is equal to

Three straight lines $l_1, l_2$ and $l_3$ are parallel and lie in the same plane. Five points are taken on each of $l_1$, $l_2$ and $l_3$. The maximum number of triangles which can be obtained with vertices at these points, is

In a polygon, no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon is 70, then the number of diagonals of the polygon is

Four speakers will address a meeting, where speaker $Q$ will always speak after speaker $P$. Then, the number of ways in which the order of speakers can be prepared is

The number of ways of arranging letters of the word HAVANA so that $V$ and $N$ do not appear together is

From the vertices of a regular polygon of 10 sides, the number of ways of selecting three vertices such that no two vertices are consecutive is

Total number of 3 letter words that can be formed from the letter of the word 'AAAHNPRRS' is equal to

Find the number of 6 digits numbers whose sum is 10 using the digits $1,2,3$ only

Seven different lecturers are to deliver lectures in seven periods of a class on a particular day. $A, B$ and $C$ are three of the lecturers. The number of ways in which a routine for the day can be made such that $A$ delivers his lecture before $B$ and $B$ before $C$, is

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy $B_{1}$ and a particular girl $\mathrm{G}_{1}$ never sit adjacent to each other, is :

The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive is

The letters of the word GHOTU is arranged alphabetically as in a dictionary. The rank of the word TOUGH is

A round table conference is to be held between 20 delegates of 2 countries. In how many ways can they be seated if two particular delegates are always together

Five distinct letters are to be transmitted through a communication channel. A total number of 15 blanks is to be inserted between the letters with atleast three between every two. The number of ways in which this can be done, is

If $N$ is the number of positive integral solution of ${x_1}{x_2}{x_3}{x_4} = 770$, then the value of $N$ is

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is

There are 3 set of parallel lines containing respectively $p$ lines, $q$ lines and $r$ lines respectively. The greatest number of parallelograms that can be formed by the system

The exponent of 12 in 50! is