HARD

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In how many ways can the letter of the word INDEPENDENCE be arranged so that the words begin with P?

Important Questions on Permutation and Combination

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Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

A person writes letter to six friends and addresses the corresponding envelopes. Let

x

be the numbers of ways so that at least two of the letters are in wrong envelopes and

y

be the numbers of ways so that all the letters are in wrong envelopes. Then

x - y =

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

There are

3

sections in a question paper and each section contains

5

questions. A candidate has to answer a total of

5

questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

A group of students comprises of

5

boys and

n

girls. If the number of ways, in which a team of

3

students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is

1750,

then

n

is equal to

EASY

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

In a March Past, seven persons are standing in a row, Q is standing left to R but right to P. O is standing right to N and left to P. Similarly, S is standing right to R and left to T. Find out who is standing in the middle.

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

Suppose four balls labelled

1, 2, 3, 4

are randomly placed in boxes

B_{1}, B_{2}, B_{3}, B_{4}

. The probability that exactly one box is empty is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

Consider a class of

5

girls and

7

boys. The number of different teams consisting of

2

girls and

3

boys that can be formed from this class, if there are two specific boys

A

and

B,

who refuse to be the members of the same team, is:

HARD

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

Six cards and six envelopes are numbered

1, 2, 3, 4, 5, 6

and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and more over the card numbered

1

is always placed in envelope numbered

2

. Then the number of ways it can be done is

EASY

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

Six people are sitting in a circle. '

J

' is between '

N

' and '

O

'; '

N

' is opposite '

M

'; and '

L

' is not in either of the neighbouring seats of '

N

'. Who is opposite to '

K

EASY

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

There are

m

men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by

84

, then the value of

m

is :

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

In a group of

6

boys and

4

girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

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:

HARD

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

We will say that a rearrangement of the letters of a word has no fixed letters if, when the rearrangement is placed directly below the word, no column has the same letter repeated. For instance,

HBRATA

is a rearrangement with no fixed letters of

BHARAT

. How many distinguishable rearrangements with no fixed letters does

BHARAT

have? (The two

A's

are considered identical)

HARD

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

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

EASY

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

There are

7

greeting cards, each of a different colour and

7

envelopes of same

7

colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly

4

of the cards go into envelopes of respective colour is,

EASY

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

Six buses B1, B2, B3, B4, B5 and B6 are parked around a circular path (not necessarily in the same order). B3 is third to the right of B6. B4 is to the immediate Left of B1. B2 is second to the left of B6. How many buses are between B5 and B1?

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

If all possible numbers are formed by using the digits

1, 2, 3, 5, 7

without repetition and they are arranged in descending order, then the rank of the number

327

HARD

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

If the letters of the word

^{'} {MOTHER}^{'}

be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word

^{'} {MOTHER}^{'}

is.....

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

If there are

5

letters written to

5

different people and

5

envelopes addressed to them, then the number of ways in which these letters can be arranged so that no letter goes into its corresponding envelope is

HARD

Mathematics>Algebra>Permutation and Combination>Inclusion-Exclusion Principle

Find the largest positive integer

N

such that the number of integers in the set

{1, 2, 3, \dots, N}

which are divisible by

3

is equal to the number of integers which are divisible by

5

7

(or both).

In how many ways can the letter of the word INDEPENDENCE be arranged so that the words begin with P?

Important Questions on Permutation and Combination

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