# Permutations and Combinations

How many different arrangements can be made by using all the letters of the word (i) MONDAY; (ii) ORIENTAL? How many of these arrangements begin with A and end with N?

In how many ways can a consonant and a vowel be chosen out of the letters of each of the words (i) LOGARITHM, (ii) EQUATION?

There are 8 vacant chairs in a room. In how many ways can 5 persons take their seats?

There are 50 stations on a railways line. How many different kinds of single first class tickets must be printed so as to enable a passenger to go from one station to another?

How many different numbers of six digits can be formed with the digits 3, 1, 7, 0, 9, 5? How many of these have 0 in ten’s places?

How many different words can be formed with the letters of the word SUNDAY? How many of the words begin with N? How many begin with N and end in Y?

There are four routes for going from A to B and five routes for going from B to C. In how many different ways can a man go from A to C via B

Find how many words can be formed of the letters of the word "FAILURE". The four vowels always coming together.

In how many ways 10 examination papers be arranged so that the best and worst papers never come together.

How many numbers between 3000 and 4000 can be formed with the digits 1, 2, 3, 4, 5, 6?

### Permutations and Combinations

#### Combination: Problem 10

The staff of a bank consists of the manager, the deputy manager and 10 other officers. A committee of 4 is to be selected. Find the number of ways in...

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#### Combination: Problem 6

In how many ways can 21 white balls and 19 black balls be arranged in a row so that no two black balls may be together?

#### Combination: Problem 5

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this...

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#### Combination: Problem 3

A cricket team is to be formed consisting of 2 wicket keepers, 4 bowlers and 5 batsmen form a group of players containing 4 wicket keepers, 8 bowlers and 11...

#### Problem 28: Permutation

There are six students of whom 2 are Indians, 2 Americans and the remaining 2 are Russians. They have to stand in a line so that the two Indians are...

#### Problem 27: Permutation

If all the permutations of the letters of the word CHALK be writtern down as in a dictionary, what is the rank of the word?

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#### In how many ways can 4 men and 3 Ladies be arranged at a round table if the 3 ladies (i) never sit together, (ii) always sit together?

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#### In how many ways can 7 Indians and 6 Pakistanis sit down a round table so that no two Indians are together?

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#### In how many ways 6 men can sit at a round table so that all shall not have the same neighbors in any two arrangements?

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#### In how many ways can 8 different beads be strung on a necklace? (ii) In how many ways can 8 boys from a ring

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#### In how many ways can 10 letters be posted in 5 letter boxes?

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#### A telegraph post has five arms and each arm is capable of 4 distinct positions including the positions of rest. What is the total number of signals that can be made?

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#### Problem 29: Permutation

How many different words can be formed with the letters of HARYANA? In how many of theseH and N are together,begin with H and end with N?

#### In how many ways can 3 books on Commercial Mathematics and 5 books on Secretarial Practice be placed on a shelf so that books on the same subject always remain together? (no two books are identical).

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#### A library has 5 copies of one book, 4 copies of each of two books, 6 copies of each of three books and single copies of 8 books. In how many ways can all the books be arranged?

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#### How many permutations can be made out of the letters of the following words taken all together? (i) PERMUTATION (ii) EXAMINATION (iii) MISSISSIPPI (iv) COLLEGE

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#### How many permutations can be made out of the letters of the word INDEPENDENCE? In how many of them the vowels occur together?

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#### How many numbers greater than a million can be formed with the digits, 1, 7, 1, 0, 7, 3, 7?

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#### Find the number of all possible different words into which the word ‘INTERFERENCE’ can be converted by change of place of the letters, it being given that no two consonants are to be together.

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#### How many different words containing all the letters of the word TRIANGLE can be formed? How many of them

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#### Problem 17: Permutation

In how many ways can be letters of the word VIOLENT be arranged so that the vowels I, O, E, occupy even places only.

#### Problem 16: Permutation

Find the number of permutations of the letters of the word “SIGNAL’ such that the vowels may occupy only odd positions.

#### Problem 15: Permutation

Find the number of ways in which n books can be arranged on a shelf so that two particular books are not together.

#### Problem 14: Permutation

The figures 1, 2, 3, 4, 5 are written in every possible order. How many of the numbers so formed will be greater than 23000?

#### Problem 13: Permutation

How many numbers between 1000 and 10,000 can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9? How many of them are odd?

#### Problem 12: Permutation

Six papers are set in an examination of which two are mathematical. In how many different orders can the papers be arranged so that (i) the two mathematical papers are...

#### Problem 11: Permutation

In how many ways 8 examination papers be arranged in a line so that the best and worst papers never come together?

#### Problem 10: Permutation

How many numbers between 3000 and 4000 can be formed with the digits 1, 2, 3, 4, 5, 6?

#### Problem 9: Permutation

In how many ways 10 examination papers be arranged so that the best and worst papers never come together.

#### Problem 8: Permutation

Find how many words can be formed of the letters of the word "FAILURE". The four vowels always coming together.

#### Problem 7: Permutation

There are four routes for going from A to B and five routes for going from B to C. In how many different ways can a man go from A...

#### Problem 6: Permutation

How many different words can be formed with the letters of the word SUNDAY? How many of the words begin with N? How many begin with N and end in...

#### Problem 5: Permutation

How many different numbers of six digits can be formed with the digits 3, 1, 7, 0, 9, 5? How many of these have 0 in ten’s places?

#### Problem 4: Permutation

There are 50 stations on a railways line. How many different kinds of single first class tickets must be printed so as to enable a passenger to go from one...

#### Problem 3: Permutation

There are 8 vacant chairs in a room. In how many ways can 5 persons take their seats?

#### Problem 2: Permutation

In how many ways can a consonant and a vowel be chosen out of the letters of each of the words (i) LOGARITHM, (ii) EQUATION?

#### Problem 1: Permutation

How many different arrangements can be made by using all the letters of the word (i) MONDAY; (ii) ORIENTAL? How many of these arrangements begin with A and end with...