CBSE Class 11 Mathematics Permutations And Combinations Worksheet Set A

Question. How many positive numbers can be formed by using any number of the digits 0, 1, 2, 3 and 4; no digit being repeated in any number?
Answer : 260

Question. How many different numbers can be formed by using all the digits 1, 2, 3, 4, 3, 2, 1, so that odd digits always occupy odd places?
Answer : 18

Question. How many odd numbers less than 1000 can be formed using the digits 0, 1, 4 and 7 if repetition of digits is allowed?
Answer : 32

Question. In how many ways can five people be seated in a car with two people in the front seat and three in the rear, if two particular persons out of the five cannot drive?
Answer : 72

Question. How many even numbers of four digits can be formed with the digits 0, 1, 2, 3, 4, 5 and 6; no digit being used more than once?
Answer : 420

Question. How many even numbers are there with three digits such that if 5 is one of the digits in a number then 7 is the next digit in that number.
Answer : 365

Question. How many non-zero numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 if repetition of digits is not allowed?
Answer : 1630

Question. In how many ways can 16 rupees and 12 paise coins be arranged in a line so that no two paise coins may occupy consecutive positions?
Answer : ¹⁷C₁₂ = 6188 when all rupee coins are identical and all paise coins are identical; 16! × ¹⁷C₁₂ , if coins of same value are different.

Question. 3 women and 5 men are to sit in a row for a dinner. Find in how many ways they can be arranged so that no two women sit next to each other.
Answer : 16! × 6C₃

Question. The letters of the word OUGHT are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word TOUGH in this dictionary.
Answer : 89th

Question. If the difference permutations of all the letters of the word EXAMINATION are listed as in a dictionary, how many items are there in this list before the first word starting with E?
Answer : 907200

Question. In how many ways can 5 flags, in which 3 are red, one is white and one is blue, be arranged on a staff, one below the other, if flags of one colour are not distinguishable?
Answer : 20

Question. A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T(for Thymine) and 3 molecules of each kind. How many different such arrangements are possible in all?
Answer : 369600

Question. In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together.
Answer : 8.9 !

Question. A class consists of 40 girls and 60 boys. In how many ways can a president, vice president, treasure and secretary be chosen if the treasure must be a girl, the secretary must be a boy and a student may not hold more than one office?
Answer : 22814400

Question. Ali has 2 school bags, 3 tiffin boxes and 2 water bottles. In how many ways can he carry these items choosing one each.
Answer : 12

Question. Find n, if ^n-1P₃ : ⁿP₄ = 1 : 9 .
Answer : n = 9

Question. Find the total number of ways in which n distinct objects can be put into two different boxes so that no box remains empty.
Answer : 2ⁿ–2

Question. There are 3 nominations for the post of president, 4 for the post of vice-president and 5 for the secretary.
(i) In how many ways can candidates be selected for each of these posts ?
(ii) In how many ways can any one of these posts be filled ?
Answer : (i) 60 (ii) 12

Question. How many 3-digit numbers have exactly one of their digits as 5?
Answer : 225

Question. In how many ways can 3 people be seated in a row containing 7 seats?
Answer : 210

Question. Number 1, 2 and 3 are written on three cards. How many two digit numbers can be formed by placing two cards side by side ?
Answer : 6

Question. Find the number of numbers of 4 digits greater than 3000 that can be formed with the digits 0, 1, 2, 3, 4 and ‘5 if repetition of digits is allowed.
Answer : 647

Question. In a town, the car plate numbers contain only three or four digits, not containing the digit 0. What is the maximum number of cars that can be numbered?
Answer : 9³ + 9⁴ = 7290

Question. A person wants to go to another city by bus and return by train. He has a choice of 5 different buses and 4 trains to return. In how many ways can be perform his journey?
Answer : 20

Question. Eight children are standing in a queue.
(i) In how many ways can the queue be formed ?
(ii) How many arrangements are possible if the tallest child stands at the end of the queue ?
Answer : (i) 40320 (ii) 5040

Question. (i) Find the sum of all the four digit numbers which can be formed with the digits 0, 1, 2, and 3.
(ii) Find the sum of all the 4 digit numbers which can be fomed with the digits 1, 2, 2 and 3.
Answer : (i) 38664 (ii) 26664

Question. A gentleman has 6 friends to invite. In how many ways can he send invitation cards to them if he has three servants to carry the cards.
Answer : 729

Question. In how many ways can a student answer a set of ten true/false type question ?
Answer : 1024

Question. A teacher has to select either a boy or a girl from a class of 12 boys and 15 girls for coordinating a school function. In how many ways can she do it?
Answer : 27

Question. There are 5 routes from A to B and 3 routes from place B to place C. Find how many different routes are there from A to C via B.
Answer : 15

Question. How many numbers are there between 100 and 1000 in which all the digits are distinct ?
Answer : 648

Question. There are seven flags of different colours. A signal is generated using two flags How many different signals can be generated ?
Answer : 42

Question. There are 6 multiple choice questions in an examination. How many sequence of answers are possible, if the first three questions have 4 choices each and the next three have 5 each ?
Answer : 8000

Question. In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Answer : 33810

Question. In how many ways 4 boys and 4 girls can be seated in a row so that boys and girls are alternate?
Answer : 1152

Question. In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate?
Answer : 144

Question. How many signals can be made by hoisting 2 blue, 2 red and 5 yellow flags on a pole at the same time?
Answer : 9! / 2! 2!5!

Question. How many different signals can be made by hoisting 6 differently coloured flags one above the other when any number of them may be hoisted at once?
Answer : ⁶P₁ + ⁶P₂ + ⁶P₃ + ⁶P₄ + ⁶P₅ + ⁶P₆ + 1956

Question. In how many ways 10 Indians, 5 Amercians and 4 Englishmen can be seated in a row so that neither Americans nor Englishmen sit between Indians.
Answer : 10! 10!

Question. In a dinner party there are 10 Indians, 5 Amercians and 5 Englishmen. In how many ways can they be seated in a row so that all persons of the same nationality sit together?
Answer : 3 ! 10! 5! 5!

Question. How many ways can the letters of the word ‘VIOLENT’ be arranged so that vowels occupy only the odd places ?
Answer : 576

Question. In how many different ways can the letters of the word ‘SALOON’ be arranged if the consonants and vowels must occupy alternate places?
Answer : 36

Question. In a class of students, there are 4 girls and 6 boys. In how many ways can they be seated in a row so that all the four girls are not together.
Answer : 10! – 7! 4!

Question. Six papers are set in an examination, 2 of them in Mathematics. In how many different orders can the papers be given if two Mathematics papers are not successive?
Answer : 6! – 5! 2!

Question. A number lock on a suitcase has 3 wheels each labelled with ten digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
Answer : 720

Question. You are given 6 balls of different colours (black, white, red, green, violet, yellow), in how many ways can your arrange them in a row so that black and white balls may never come together?
Answer : 480

Question. (i) Find the number of words formed, with the letters of the word ‘DELHI’ when any letter may be repeated any number of times.
(ii) Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word ‘ROSE’ where
(a) the repetition of the letters is not allowed.
(b) repetition of the letters is allowed.
Answer : (i) 5⁵ = 3125 (ii) (a) 24 (b) 256

Question. How many words can be formed by using the letters of the word ‘BHARAT’ ? How many of these words will not contain B and H together? How many of these start with B and end with T?
Answer : 360; 240; 12

Question. In how many ways can 4 boys and 3 girls be seated in a row so that no two girls are together?
Answer : 1440