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Statement 1: If a polygon has total $66$ diagonals, then the total number of its sides are $12$ .

Statement 2: The total number of ways of selecting $2$ points out of $n$ non-collinear points is ${}^{n}C_{2}$ .

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Important Questions on Permutation and Combination

HARD

Mathematics>Algebra>Permutation and Combination>Combinations

The value of

\sum_{r = 1}^{15} r^{2} (\frac{^{15} C_{r}}{^{15} C_{r - 1}})

is equal to:

EASY

Mathematics>Algebra>Permutation and Combination>Combinations

A password is set with

3

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

HARD

Mathematics>Algebra>Permutation and Combination>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?

EASY

Mathematics>Algebra>Permutation and Combination>Combinations

The Number of ways of choosing

10

objects out of

31

objects of which

10

are identical and the remaining

21

are distinct, is:

HARD

Mathematics>Algebra>Permutation and Combination>Combinations

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

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Combinations

A committee of

11

member is to be formed from

8

males and

5

females. If

m

is the number of ways the committee is formed with at least

6

males and

n

is the number of ways the committee is formed with at least

3

females, then

MEDIUM

Mathematics>Algebra>Permutation and Combination>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

EASY

Mathematics>Algebra>Permutation and Combination>Combinations

The number of ways a committee of

4

people can be chosen from a panel of

10

people is

MEDIUM

Mathematics>Algebra>Permutation and Combination>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

Mathematics>Algebra>Permutation and Combination>Combinations

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

and

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

,

then

n =

HARD

Mathematics>Algebra>Permutation and Combination>Combinations

a, b

and

c

are the greatest values of

{}^{19}{C_{p}}, {}^{20}{C_{q}}

and

{}^{21}{C_{r}}

respectively, then:

EASY

Mathematics>Algebra>Permutation and Combination>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

Mathematics>Algebra>Permutation and Combination>Combinations

Total number of

6

-digit numbers in which only and all the five digits

1, 3, 5, 7

and

9

appears, is

HARD

Mathematics>Algebra>Permutation and Combination>Combinations

Let

S = \{1,2, 3, \dots . 9\}

. For

k = 1,2, \dots 5,

let

N_{k}

be the number of subsets of

S

, each containing five elements out of which exactly

k

are odd. Then

N_{1} + N_{2} + N_{3} + N_{4} + N_{5} =

EASY

Mathematics>Algebra>Permutation and Combination>Combinations

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Combinations

Let

n > 2

be an integer. Suppose that there are

n

Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only. Further, each pair of the nearest station is connected by blue line, whereas all remaining pairs of stations are connected by red line. If number of red lines is

99

times the number of blue lines, then the value of

n

MEDIUM

Mathematics>Algebra>Permutation and Combination>Combinations

The number of positive integers less than

1000

having only odd digits is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Combinations

The number of diagonals of a polygon with

15

sides is

HARD

Mathematics>Algebra>Permutation and Combination>Combinations

If in a regular polygon the number of diagonals is

54

, then the number of sides of this polygon is:

MEDIUM

Mathematics>Algebra>Permutation and Combination>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

Statement 1: If a polygon has total 66 diagonals, then the total number of its sides are 12. Statement 2: The total number of ways of selecting 2 points out of n non-collinear points is C2n.

Important Questions on Permutation and Combination

Learn and Prepare for any exam you want !

Statement 1: If a polygon has total $66$ diagonals, then the total number of its sides are $12$ .

Statement 2: The total number of ways of selecting $2$ points out of $n$ non-collinear points is ${}^{n}C_{2}$ .