Permutations and Combinations

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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.

Problems: Permutations and Combinations

Combination: Problem 11

A council consists of 10 members, 6 belonging to the party A and 4 to the party B. In how many ways ...

Combination: Problem 10

The staff of a bank consists of the manager, the deputy manager and 10 other officers. A committee o...

Combination: Problem 9

From 7 gentlemen and 4 ladies a committee of 5 is to be formed in how many ways can this be done so ...

Combination: Problem 8

Out of 5 males and 6 females, a committee of 5 is to be formed. Find the number of ways in which it ...

Combination: Problem 7

Find out the number of ways in which a cricket team consisting of 11 players can be selected from 14...

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 bal...

Combination: Problem 5

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to...

In how many ways can you choose six out of nine questions? In how many of these ways the first question is always excluded? In how many ways the first and second questions are always...

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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 ...

Problem 28: Permutation

There are six students of whom 2 are Indians, 2 Americans and the remaining 2 are Russians. They hav...

Problem 27: Permutation

If all the permutations of the letters of the word CHALK be written down as in a dictionary, what is...

Seven persons sit in a row. Find the total number of searing arrangements, if

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Problem 27: Permutation

A family consisting of an old man, 6 adults and 4 children, is to be seated in a row for dinner. The...

A guard of 15 men is formed from a group of m soldiers in all possible ways. Find

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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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Problem 18: Permutation

(a) In how many ways can 8 different beads be strung on a necklace? (b) In how many ways can 8 boys ...

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 ...

Problem 21: Permutation

Find the number of all possible different words into which the word ‘INTERFERENCE’ can be converted ...

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

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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 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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Problem 19: Permutation

A library has 5 copies of one book, 4 copies of each of two books, 6 copies of each of three books, ...

Problem 14: Permutation

The figures 1, 2, 3, 4, 5 are written in every possible order. How many of the numbers so formed wil...

Problem 10: Permutation

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

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? Ho...

Problem 17: Permutation

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

Problem 20: Permutation

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

Problem 12: Permutation

Six papers are set in an examination of which two are mathematical. In how many different orders can...

Problem 16: Permutation

In how many ways can 3 books on Commercial Mathematics and 5 books on Secretarial Practice be placed...

Problem 15: Permutation

Find the number of ways in which n books can be arranged on a shelf so that two particular books are...

Problem 9: Permutation

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

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) L...

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

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Problem 8: Permutation

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

Problem 1: Permutation

How many different arrangements can be made by using all the letters of the word (i) MONDAY; (ii) OR...

Problem 6: Permutation

How many different words can be formed with the letters of the word SUNDAY? How many of the words be...

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...

Problem 4: Permutation

There are 50 stations on a railways line. How many different kinds of single first class tickets mus...

Problem 3: Permutation

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

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 diffe...

Permutations and Combinations

Problems: Permutations and Combinations

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