If A = 1 , 2 , 3 , 4 … … n and B ⊆ A ; C ⊆ A , then find the number of ways of selecting i Sets B and C i i Order pair of B and C such that B ∩ C = ϕ i i i Unordered pair of B and C such that B ∩ C = ϕ i v Ordered pair of B and C such that B ∪ C = A and B ∩ C = ϕ v Unordered pair of B and C such that B ∪ C = A , B ∩ C = ϕ v i Ordered pair of B and C such that B ∩ C is a singleton

Set B can be chosen in C 0 n + C 1 n + . . . . + C n n = 2 n Similarly, set C can be chosen in C 0 n + C 1 n + . . . . + C n n = 2 n So, total number of ways is 2 n × 2 n . If B ∩ C = ϕ then the number of ways of choosing is C 0 n × 2 n + C 1 n × 2 n - 1 + C 2 n × 2 n - 2 + . . . . + C n n × 2 n - n = 1 + 2 n = 3 n If B , C is ordered pair, the number of ways is 3 n . here, if both set is null set, then it can be ordered pair or unordered pair. So, total number of ordered pair is 3 n - 1 2 + 1 . If B ∪ C = A & B ∩ C = ϕ , then the number of ways is C 0 n · 1 + C 1 n · 1 + . . . + C n n · 1 = 2 n If this is ordered pair, then the number of ways is 2 n 2 !

EASY

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IMPORTANT

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A committee of $6$ is to be chosen from $10$ persons with the condition that if a particular person $' A'$ is chosen, then another particular person $B$ must be chosen.

Important Questions on Permutation and Combination

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 15

In how many ways we can select

5

cards from a deck of

52

cards, if each selection must include at least one king.

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 16

How many four digit natural numbers not exceeding the number

4321

can be formed using the digits

1, 2, 3, 4

if repetition is allowed?

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 17

How many different permutations are possible using all the letters of the word

MISSISSIPPI

, if no two

I' s

are together?

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 18

A = \{1, 2, 3, 4 \dots \dots n\}

and

B \subseteq A; C \subseteq A,

then find the number of ways of selecting

(i)

Sets

B

and

C

(i i)

Order pair of

B

and

C

such that

B \cap C = ϕ

(i i i)

Unordered pair of

B

and

C

such that

B \cap C = ϕ

(i v)

Ordered pair of

B

and

C

such that

B \cup C = A

and

B \cap C = ϕ

(v)

Unordered pair of

B

and

C

such that

B \cup C = A, B \cap C = ϕ

(v i)

Ordered pair of

B

and

C

such that

B \cap C

is a singleton

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 19

For a set of six true or false statements, no student in a class has written all correct answers and no two students in the class have written the same sequence of answers. What is the maximum number of students in the class, for this to be possible.

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 20

How many arithmetic progressions with

10

terms are there, whose first term is in the set

\{1, 2, 3, 4\}

and whose common difference is in the set

\{3, 4, 5, 6, 7\} ?

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 21

Find the number of all five-digit numbers which have atleast one-digit repeated.

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-1>Q 22

There are

3

white,

4

blue and

1

red flowers. All of them are taken out one by one and arranged in a row in the order. How many different arrangements are possible (flowers of same colurs are similar)?

A committee of 6 is to be chosen from 10 persons with the condition that if a particular person 'A' is chosen, then another particular person B must be chosen.

Important Questions on Permutation and Combination

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A committee of $6$ is to be chosen from $10$ persons with the condition that if a particular person $' A'$ is chosen, then another particular person $B$ must be chosen.