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

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Important Questions on Permutation and Combination

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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>Permutations when All the Objects are Distinct

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

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

All possible numbers are formed using the digits

1, 1, 2, 2, 2, 2, 3, 4, 4

taken all at a time. The number of such numbers in which the odd digits occupy even places is

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

If all the words (with or without meaning) having five letters, formed using the letters of the word

S M A L L

and arranged as in a dictionary; then the position of the word

S M A L L

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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>Permutations when All the Objects are Distinct

How many numbers of four digits can be made by using the digits $3, 5, 6, 7,$ and $9$ ? (Repetition of digits is not allowed)

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

Find the number of ways of preparing a chain with

6

different coloured beads.

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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>Permutations when All the Objects are Distinct

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>Permutations when All the Objects are Distinct

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

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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:

EASY

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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>Permutations when All the Objects are Distinct

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:

HARD

Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

The number of

4

digit numbers without repetition that can be formed using the digits

1, 2, 3, 4, 5, 6, 7

in which each number has two odd digits and two even digits is

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

In how many ways the letters of word 'MACHINE' can be arranged so that vowels will always be together?

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Mathematics>Algebra>Permutation and Combination>Permutations when All the Objects are Distinct

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>Permutations when All the Objects are Distinct

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>Permutations when All the Objects are Distinct

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

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

Important Questions on Permutation and Combination

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