Circular Permutation

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

The number of ways that a circle can be made out of $6$ black and $4$ white men standing on a ring, so that all the white men come together is

How many necklaces of $10$ beads each can be made from $20$ beads of different colours?

The following table shows the number of students wearing particular colour.

In how many ways the students who are wearing Pink and Yellow sit around the table so that no two students sit together who are wearing Pink.

The number of ways in which $5$ boys and $4$ girls can be arranged on a circular table such that no two girls sit together and two particular boys are always together is

$15$ persons are siting down at random at a round table, then the probability that there are $4$ persons in between two particular person $A \& B$ is

A class is composed of $2$ brothers and $8$ other boys. The combinations by which the boys can be seated at a round table so that the $2$ brothers are not seated beside each other is

Cotyledons are also called-

The letters of the word "QUESTION" are arranged in a row at random. The probability that there are exactly two letters between Q and S is

Twenty persons among whom $A$ and $B$, sit at random around a round table, then the probability that there are any $6$ persons between $A$ and $B$ is

The number of different garlands, that can be formed using $3$ flowers of first kind and $3$ flowers of second kind, is

$20$ persons are to be seated around a circular table. Out of these$20$, two are brothers. Then number of arrangements in which there will be at least three persons between the brothers is

Number of ways in which 5 boys and 4 girls can be arranged on a circular table such that no two girls sit together and two particular boys are always together.

$7$ boys be seated at a round table. $x$ is the number of ways in which two particular boys are next to each other,$y$ is number of ways in which they are separated. Then $x+y$ is

The number of different necklaces that can be formed by using $2n$ identical diamonds and $3$ different jewels -

The number of ways in which $5$ keys be put in a ring is 

If eleven member of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangements is

$20$persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

$20$ persons are invited to a party. the number of different ways can they and the host is seated at the circular table if the two particular persons are to be seated on either side of the host

The number of ways that 8 beads of different colures be string as a necklace, is