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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from $10$ white, $9$ green and $7$ black balls is

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Important Questions on Permutation and Combination

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 19

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

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 20

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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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 21

If all the words (with or without meaning) having five letters, formed using the letters of the word

SMALL

and arranged as in a dictionary; then the position of the word

SMALL

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 22

A man

X

has

7

friends,

4

of them are ladies and

3

are men. His wife

Y

also has

7

friends,

3

of them are ladies and

4

are men. Assume

X

and

Y

have no common friends. Then, the total number of ways in which

X

and

Y

together can throw a party inviting

3

ladies and

3

men, so that

3

friends of each of

X

and

Y

are in this party, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 23

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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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 24

Let

S

be the set of all triangles in the

x y

- plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in

S

has area

50

sq. units, then the number of elements in the set

S

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 25

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

th 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}

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Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-4>Q 1

How many positive integers are there such that

n

is a divisor of one of the numbers

10^{40}, 20^{30} ?

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

Important Questions on Permutation and Combination

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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from $10$ white, $9$ green and $7$ black balls is