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The number of ways in which a person can choose $3$ squares on a chessboard such that one of the squares has its sides common to other two squares is equal to____

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Important Questions on Permutations and Combinations

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 68

Number of octagons that can be formed by using vertices of

20

sided polygon such that no side of octagon is common with side of polygon is given by

{}^{13}C_{r_{1}} - {}^{11}C_{r_{2}}

then minimum value of

r_{1} + r_{2}

is equal to___

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 1

If one quarter of all the subsets containing three elements of the integers

1, 2, 3, . . . ., m

contain the integer

5

, then

m

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 2

Let

y

be an element of the set

A = \{1, 2, 3, 5, 6, 10, 15, 30\}

and

x_{1}, x_{2}, x_{3}

be integers such that

x_{1} x_{2} x_{3} = y

,then number of positive integral solution of

x_{1} x_{2} x_{3} = y

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 3

The number of divisors of the form

4 k + 2, k \geq 0

of the integer

240

is:-

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 4

There are

3

apartments

A, B

and

C

for rent in a building. Each apartment will accept either

3

4

occupants. The number of ways of renting the apartments to

10

students

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 5

A double-decker bus has

5

empty seats in the upper deck and

5

empty seats in the lower deck.

10

people board the bus of which

2

are old people and

3

are children. The children refuse to take seats lower deck while old people insist to stay lower deck. How many different sitting arrangements of the people are possible

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Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 7

There are

6

letters and

6

directed envelopes. The number of ways in which

4

letters are rightly placed and

2

letters are wrongly placed, is

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 7 - Permutations and Combinations>Assignment>Q 8

Out of

6

consonants and

5

vowels, number of words, that can be made each containing

4

consonants and

2

vowels, is

The number of ways in which a person can choose 3 squares on a chessboard such that one of the squares has its sides common to other two squares is equal to____

Important Questions on Permutations and Combinations

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The number of ways in which a person can choose $3$ squares on a chessboard such that one of the squares has its sides common to other two squares is equal to____