Permutation and Combination Questions

Permutation and Combination is an indispensable part of almost all the popular scholastic and competitive exams like GMAT, GRE, SAT exam, SSC CGL, etc. In order to achieve a perfect score in examinations, you must prepare this topic in detail as it requires the application of a multitude of tricky concepts and formulas. To help you go through this topic, here are some permutation and combination questions based on distinct situations. So pull up your socks and let’s get started! 

What is Permutation and Combinations?

While permutation refers to a particular arrangement of a set of objects in a defined order or a process of arranging numbers or letters in a sequence, combination refers to selecting items from a combination or selection of all or part of a set of objects, without giving regard to the order in which the objects are selected.  

MCQ

Let’s solve a few MCQs before moving on to the practice questions for Permutation and Combinations –

Permutation and Combination Questions – SET 1

• In a competitive exam, Rohit was asked to answer 7 questions out of 12, which were divided into two groups of maths and science having 6 questions each. Rohit was not allowed to attempt more than 5 questions from both the groups. Find out the total number of different ways of attempting the question.  

• During a birthday party game, out of 6 girls and 4 boys, 4 kids were to be selected. Find out the total number of ways in which selection should be done so that at least 1 boy is chosen. 

• Find out the ways in which the letters of the word ‘ENCYCLOPEDIA’ can be placed so that the vowels always come together?

• In how many ways the letters of the word ’MISSISSIPPI’ can be arranged so that no two same alphabets come together.

• Find out the ways in which a panel of 3 judges can be formed from a group of 8 people in which there are 3 doctors, 3 engineers, and 2. The panel must include at least one doctor. 

Questions – SET 2

• Find out how many words having 4 consonants and 3 vowels can be formed from a group of 8 consonants and 5 vowels.

• There are 5 different types of flags available- F1, F2, F3, F4, and F5 using which, a signal can be formed. Determine how many signals using 2 flags (Different) can be made out of these 5 flags. 

• Using the digits from 0-7, how many telephone numbers can be formed starting from 98 if all the digits only appear once. 

• Determine the ways in which the 5 black shoes, 3 brown shoes, and 2 white shoes can be placed in a row if no two shoes of the same colour are put together. 

• For a corporate task, 5 persons are to be chosen to form a team. The team members have to be chosen from a group of 8 women and 6 men. Also, in the chosen group, there should be at least 3 men. In how many possible ways can the team be formed?

Permutation and Combination Questions – SET 3

• Find the total number of positive integers which are greater than 8000 but less than 7000 and are divisible by 4, in a way such that no digit is repeated. 

• During the final examinations, a student is instructed to answer 4 problems out of 5, in which the 1st and 2nd are mandatory. Find out the number of choices that a student can make.

• Whilst playing musical chairs on Sita’s birthday, there were 8 chairs, each numbered between 1 to 8. Out of all, 2 girls sat on the chairs which were between 1 to 4 number and then the boys chose from the ones which were left. Find out the total possible arrangements.

• A lady’s purse contains 4 white, 3 black, and 2 red ribbons. She was picking out three of them together, determine that in how many ways she can draw ribbons from her purse so that at least one black ribbon comes out every time.

• Arrange the letter of the word ‘MAINTENANCE’ such that, in how many ways:

The words formed to start with T	Vowels never occur together
All the vowels are placed together	The words begin with A and end with  E

Permutation and Combinations – Set 4

• In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
•  How many words with or without meaning, can be formed by using all the letters of the word, ‘DELHI’ using each letter exactly once?
• In how many different ways can the letters of the word ‘COOPERATION’ be arranged so that the vowels always come together?

Permutation and Combinations – Set 5

• Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
•  In how many different ways can the letters of the word ‘OSMOSIS’ be arranged so that the vowels always come together?
• How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
• How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘ALGORITHMS’, if repetition of letters is not allowed?

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