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$7$ 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

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Important Questions on Permutation and Combination

MEDIUM

Mathematics>Algebra>Permutation and Combination>Circular Permutation

Two girls and four boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?

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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}

EASY

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of all

3 -

digits numbers

a b c

(in base

10

) for which

10

EASY

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

How many natural numbers

n

are there such that

n! + 10

is a perfect square ?

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 _____

EASY

Mathematics>Algebra>Permutation and Combination>Circular Permutation

The sum of the digits in the unit's place of all the

4

- digit numbers formed by using the numbers

3, 4, 5

and

6

, without repetition is :

EASY

Mathematics>Algebra>Permutation and Combination>Circular Permutation

Find the number of ways of preparing a chain with

6

different coloured beads.

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.

MEDIUM

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:

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of distinct primes dividing

12! + 13! + 14!

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The total number of permutations of

n (> 1)

different things taken not more than

r

at a time, when each thing may be repeated any number of times is

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Mathematics>Algebra>Permutation and Combination>Circular Permutation

The largest non-negative integer

k

such that

24^{k}

divides

13!

EASY

Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of

6

digit number that can be formed using the digits

0, 1, 2, 5, 7

and

9

which are divisible by

11

and no digit is repeated is:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Circular Permutation

The number of four-digit numbers strictly greater than

4321

that can be formed using the digit

0,1, 2,3, 4,5

(repetition of digits is allowed) is:

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

EASY

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

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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

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

Important Questions on Permutation and Combination

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$7$ 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