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 included?
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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...
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...
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...
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 ...
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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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...
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...
Minhajur Rahaman
