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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

In a group of

8

girls, two girls are sisters. The number of ways in which the girls can sit so that the two sisters are not sitting 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

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

The number of four-letter words that can be formed with letters

a, b, c

such that all three letters occur is

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

The number of ways in which

3

prizes can be distributed to

4

children, so that no child gets all the three prizes, are

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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 :

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

The number of permutations of the letters

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}

in which the first letter

a_{1}

does not occupy the first position (from the left) and the second letter

a_{2}

does not occupy the second position (from the left) is

HARD

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

If all the seven letters of the word LEADING are permuted in all possible ways and the words thus formed are arranged as in the dictionary order, then the word in

2017^{th}

place is

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

The number of all

3 -

digits numbers

a b c

(in base

10

) for which

10

HARD

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 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:

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

Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated is

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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

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

Letters in the word

H U L U L U L U

are rearranged. The probability of all three

L

being together is

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

5

boys of class

VI

6

boys of class

VII

and

7

boys of class

VIII

sit in a row. The number of ways they can sit so that boys of the same class sit together is

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

The number of ways in which

5

girls and

3

boys can be seated in a row so that no two boys are together is

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

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:

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

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.

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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:

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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:

MEDIUM

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?

P, Q, R and S have to give lectures to an audience. The organizer can arrange the order of their presentation in

Important Questions on Permutation and Combination

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