Circular Permutation

The number of ways of arranging $7$ persons on a round table such that $2$ particular persons may not sit together is______.

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

In a round-table conference of $10$ representatives from $10$ countries, two particular representatives must take there seats side by side. In how many ways this can be arranged?

In how many ways $4$ gentlemen and $4$ ladies may be arranged to sit around a circular table such that no two woman may sit side by side?

In how many ways $6$ boys and $4$ girls may be arranged to sit around a circular table such that no two girls may sit side by side?

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

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

The number of ways of arranging $7$ persons on a round table such that $2$ particular persons may not sit together is______.

If $N$ denotes the number of different selections of 5 letters from the word $\mathbf{W}=$ MISSISSIPPI, then N belongs to the set:

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 

The number of ways in which seven persons can be arranged at a round table, if two particular persons may not sit together 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?