HARD

Earn 100

$5$ boys $(B_{1}, B_{2}, B_{3}, B_{4}$ and $B_{5})$ and $5$ girls $(G_{1}, G_{2}, G_{3}, G_{4}$ and $G_{5})$ are to be seated around a round table such that boy and girl sit alternately and $B_{1}$ does not sit beside $G_{i} \forall i \in \{1, 2, 3, 4, 5\} .$ If the number of such arrangements is $N$ , then the sum of digits of $N$ is equal to

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Important Questions on Permutation and Combination

MEDIUM

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

HARD

Mathematics>Algebra>Permutation and Combination>Circular Permutation

There are

10

red and

5

yellow roses of different sizes. If

x

is the number of garlands that can be formed with all these flowers so that no two yellow roses come together and

y

is the number of garlands formed with all these flowers so that all the red roses coming together, then

\frac{2 (x - y)}{10!} =

EASY

Mathematics>Algebra>Permutation and Combination>Circular Permutation

{}^{56}{P_{r + 6}} : {}^{54}{P_{r + 3} = 30800 : 1}

,

then

r

is equal to

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

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

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

From

6

different novels and

3

different dictionaries,

4

novels and

1

dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements 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

How many ways are there to arrange the letters of the word

EDUCATION

so that all the following three conditions hold?
- the vowels occur in the same order

(EUAIO),

- the consonants occur in the same order

(DCTN),

- no two consonants are next to each other.

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

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:

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?

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 :

HARD

Mathematics>Algebra>Permutation and Combination>Circular Permutation

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

HARD

Mathematics>Algebra>Permutation and Combination>Circular Permutation

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

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:

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

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

5 boys B1, B2, B3, B4 and B5 and 5 girls G1,G2,G3,G4 and G5 are to be seated around a round table such that boy and girl sit alternately and B1 does not sit beside Gi∀i∈1,2,3,4,5. If the number of such arrangements is N, then the sum of digits of N is equal to

Important Questions on Permutation and Combination

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