Circular Permutation

The number of circular permutations of $7$ different things, taken $5$ at a time, when clockwise and anticlockwise orders are not different is

The number of circular permutations of $6$ different things, taken $3$ at a time, when clockwise and anticlockwise orders are as different is

How many garlands of $4$ flowers each can be made from $7$ flowers of different colours?

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

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

$15$ 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

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

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

$20$ 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 -

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 of arranging $8$ men and $4$ women around a circular table such that no two women can sit together, is