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The total number of integers between $1 & 3600$ (both excluded), that are relatively prime to $3600$

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Important Questions on Permutation and Combination

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

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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)

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

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

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

MEDIUM

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

The number of integers greater than

6000

that can be formed, using the digits

3, 5, 6, 7

and

8

, without repetition is

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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).

MEDIUM

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

The number of natural numbers less than

7000

which can be formed by using the digits

0, 1, 3, 7, 9

(repetition of digits allowed) is equal to:

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 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

A debate club consists of

6

girls and

4

boys. A team of

4

members is to be selected from this club including the selection of a captain (from among these

4

members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team 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

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

{\sum_{i = 1}^{20} (\frac{^{20} C_{i - 1}}{^{20} C_{i} +^{20} C_{i - 1}})}^{3} = \frac{k}{21},

then

k

equals

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:

EASY

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

Consider three boxes, each containing

10

balls labelled

1, 2, \dots ., 10

. Suppose one ball is randomly drawn from each of the boxes. Denote by

n_{i}

, the label of the ball drawn from the

i^{t h}

box,

(i = 1, 2, 3)

. Then, the number of ways in which the balls can be chosen such that

n_{1} < n_{2} < n_{3}

is :

EASY

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

The number of ways of selecting

15

teams from

15

men and

15

women, such that each team consists of a man and a woman is

HARD

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

Let

T_{n}

be the number of all possible triangles formed by joining vertices of an

n

-sided regular polygon. If

T_{n + 1} - T_{n} = 10

, then the value of

n

is :

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,

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

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 :

The total number of integers between 1 & 3600 (both excluded), that are relatively prime to 3600

Important Questions on Permutation and Combination

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The total number of integers between $1 & 3600$ (both excluded), that are relatively prime to $3600$