Permutation and combination practice · Mixed difficulty

The number of ways in which 6 different beads can be string into a necklace is

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

The number of ways in which you can put five beads of five different colours to form a necklace is:

Five persons are to address a meeting. If a specified speaker is to speak before another specified speaker, find the number of ways in which this could be arranged. In how many of these arrangements will the first speaker come immediately before the second?

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

In how many ways a garland can be made from exactly 10 flowers?

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is

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

The number of ways in which 5 pictures can be hung from 7 picture nails on the wall 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

How many nine digit numbers can be formed by using the digits $2,2,3,3,5,5,8,8,8$ so that the odd digits occupy even positions?

Total number of divisors of $n=2^5 \cdot 3^4 \cdot 5^{10} \cdot 7^6$ that are of the form $4 \lambda+2, \lambda \geq 1$, is equal to

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 4-digit even numbers that can be formed using $0,1,2,3,4,5,6$ without repetition 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

Seven women and seven men are to sit round a circular table such that there is a man on either side of every women; the number of seating arrangements 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

In a class of 10 students there are 3 girls students. The number of ways in which they can be arranged in a row, so that no two girls are consecutive is $k(8!),$ then $k$ is equal to

Let $A$ be a set containing $n$ elements. The number of ways of choosing two subsets $P$ and $Q$ of $A$ such that $P \cap Q=\phi$ is

The number of five digits numbers that can be formed without any restriction, is

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

Seven atheletes are participating in a race. In how many ways can the first three prizes be won?

The number of ways in which the letters of the word ARRANGE be arranged so that "neither two A's nor two R's are together

How many numbers of 6 digits can be formed from the digits of the number 112233?

The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is