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There are five main roads between the cities $A$ and $B$ , and four between $B$ and $C$ . In how many ways can a person drive from $A$ to $C$ and return, going through $B$ on both trips without driving on the same road twice?

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Important Questions on Permutation and Combination

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 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

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

The number of diagonals of a polygon with

15

sides is

EASY

Mathematics>Algebra>Permutation and Combination>Combinations

The value of

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

EASY

Mathematics>Algebra>Permutation and Combination>Combinations

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

and

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

,

then

n =

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 :

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:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Combinations

The number of selection of

n

objects from

2 n

objects of which

n

are identical and the rest are different, is

MEDIUM

Mathematics>Algebra>Permutation and Combination>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

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?

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

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

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:

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?

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

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} =

MEDIUM

Mathematics>Algebra>Permutation and Combination>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

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

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

There are five main roads between the cities A and B, and four between B and C. In how many ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice?

Important Questions on Permutation and Combination

Learn and Prepare for any exam you want !

There are five main roads between the cities $A$ and $B$ , and four between $B$ and $C$ . In how many ways can a person drive from $A$ to $C$ and return, going through $B$ on both trips without driving on the same road twice?