EASY

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In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be formed from four chemical engineers and three mechanical engineers?

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Important Questions on Counting Principles

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

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

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

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

HARD

Aptitude>Arithmetic>Counting Principles>Combinations

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 :

HARD

Aptitude>Arithmetic>Counting Principles>Combinations

The number of noncongruent integer-sided triangles whose sides belong to the set

{10, 11, 12, . . . . . ., 22}

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

The value of

{}^{16}C_{9} + {}^{16}C_{10} - {}^{16}C_{6} - {}^{16}C_{7}

HARD

Aptitude>Arithmetic>Counting Principles>Combinations

If in a regular polygon the number of diagonals is

54

, then the number of sides of this polygon is:

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

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

Aptitude>Arithmetic>Counting Principles>Combinations

A password is set with

3

distinct letters from the word LOGARITHMS. How many such passwords can be formed?

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

The number of selection of

n

objects from

2 n

objects of which

n

are identical and the rest are different, is

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

In order to get through in an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails. The number of ways in which he can fail, in this examination is

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

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:

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

Total number of

6

-digit numbers in which only and all the five digits

1, 3, 5, 7

and

9

appears, is

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

{{}^{n}C}_{r - 1} = 36, {{}^{n}C}_{r} = 84

and

{{}^{n}C}_{r + 1} = 126

,

then

n =

HARD

Aptitude>Arithmetic>Counting Principles>Combinations

Let

A = \{x_{1}, x_{2}, \dots, x_{7}\} and B = \{y_{1}, y_{2}, y_{3}\}

be two sets containing seven and three distinct elements respectively. Then the total number of functions

f : A \to B

that are onto, if there exist exactly three elements

x

A

such that

f (x) = y_{2},

is equal to:

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

The number of diagonals of a polygon with

15

sides is

HARD

Aptitude>Arithmetic>Counting Principles>Combinations

In a tournament with five teams, each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point, while the losing team scores zero. Which of the following is NOT necessarily true?

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

The least value of a natural number

n

such that

(\frac{n - 1}{5}) + (\frac{n - 1}{6}) < (\frac{n}{7})

, where

(\frac{n}{r}) = \frac{n!}{(n - r)! r!}

, is

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

Let

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n},

where

C_{r} = {}^{n}C_{r}

and

(C_{0} + C_{1}) (C_{1} + C_{2}) \dots (C_{n - 1} + C_{n}) = A C_{1} C_{2} \dots C_{n}

, then for

n = 5, A

is equal to

EASY

Aptitude>Arithmetic>Counting Principles>Combinations

In how many ways a team of $5$ members can be chosen from $8$ members?

MEDIUM

Aptitude>Arithmetic>Counting Principles>Combinations

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

In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be formed from four chemical engineers and three mechanical engineers?

Important Questions on Counting Principles

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