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Calculate circular permutation of $6$ diamonds in a necklace.

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Important Questions on Permutation and Combination

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

f = (\begin{matrix} 1 \\ 3 \end{matrix} \begin{matrix} 2 \\ 4 \end{matrix} \begin{matrix} 3 \\ 6 \end{matrix} \begin{matrix} 4 \\ 7 \end{matrix} \begin{matrix} 5 \\ 5 \end{matrix} \begin{matrix} 6 \\ 1 \end{matrix}) \in S_{6}

then

f^{- 1}

HARD

Mathematics>Algebra>Permutation and Combination>Circular Permutation

Five persons

A, B, C, D

and

E

are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of ways, in which

5

girls and

7

boys can be seated at a round table so that no two girls sit together is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

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

G_{1}

never sit adjacent to each other, is:

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Mathematics>Algebra>Permutation and Combination>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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Circular Permutation

20

persons are invited for a party. The number of ways in which they and the host can seated at a circular table, if two particular persons be seated on either side of the host is equal to

EASY

Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of ways

5

boys and

5

girls can be seated at a round table, so no two boys are adjacent is _____

MEDIUM

Mathematics>Algebra>Permutation and Combination>Circular Permutation

A round table conference is attended by

3

Indians,

3

Chinese,

3

Canadians and

2

Americans. Find the number of ways of arranging them at the round table so that the delegates belonging to same country sit together.

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

Find the number of ways of preparing a chain with

6

different coloured beads.

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

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

HARD

Mathematics>Algebra>Permutation and Combination>Circular Permutation

Six persons

A, B, C, D, E

and

F

are to be seated at a circular table facing towards the centre. Then the number of ways that can be done if

A

must have either

E

F

on his immediate right and

E

must have either

F

D

on his immediate right, is

HARD

Mathematics>Algebra>Permutation and Combination>Circular Permutation

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

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of ways in which

5

beads, chosen from

8

different beads be threaded onto a ring, is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

Number of ways in which

2

Indians,

3

Americans,

3

ltalians and

4

Frenchmen can be seated on a circle, if the people of the same nationality sit together, is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of ways in which

8

different flowers can be strung to form a garland so that

4

particular flowers are never separated, is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of different garlands, that can be formed using

3

flowers of first kind and

3

flowers of second kind, is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of ways in which

6

red roses and

3

white roses (all roses different) can form a garland so that all the white roses come together, is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of ways in which

4

boys and

4

girls can stand in a circle so that each boy and each girl is one after the other, is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Circular Permutation

If the total number of m elements subsets of the set A = {a₁, a₂, a₃, ... , a_n} is λ times the number of m elements subsets containing a₄, then n is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

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

Calculate circular permutation of 6 diamonds in a necklace.

Important Questions on Permutation and Combination

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Calculate circular permutation of $6$ diamonds in a necklace.