Permutations and Combinations MCQ questions form an essential quotient of the majority of competitive exams across the country. It forms an important part of those entrance exams that are aimed to test the understanding of a candidate’s STEM concepts, such as GATE, NIELIT, SSC JE. Permutations and combinations refer to the different number of ways in which any particular group of objects can be represented by first selecting them in a defined set and by subsequently forming subsets out of them.
It presents us with a defined framework with which we can suitably arrange a specific group of data. While permutations refer to the act of selecting the objects or data from the given group of data, combinations refer to the order in which the representation of these objects and data takes place. Permutations and combinations GATE questions span across all its various categories, including GATE ECE, GATE CSE, GATE Civil, GATE Mechanical, and GATE Electrical.
Important Permutations and Combinations Topics for GATE
The permutations and combinations GATE syllabus comprises the following important topics:
In the field of combinatorics, the addition principle or rule or sum constitutes a fundamental counting principle which states the idea that if we have A number of ways of doing an event and B number of ways of completing another separate event and it is not possible to accomplish both at the same time, then we have A+B ways at our disposal to select one of the processes. Alternatively, if one action takes place in A ways and another second action with no consequences in common occurs in B ways, then the first or the second event can take place in A+B ways. It forms the basis for solving Permutation and Combination Questions.
In the field of combinatorics, the multiplication principle or rule of the product constitutes a fundamental counting principle which states the idea that if we have A number of ways of doing an event and B number of ways of completing another separate event, then we have A x B number of ways at our disposal for performing both the events. Alternatively, if one action takes place in 'A' number of ways and another second action occurs in B ways post the occurrence of the first event, then the two events can occur in A x B ways. It forms the basis for solving Permutation and Combination Questions.
It refers to the action of arranging all the constituent members of a set or group of data into a defined sequence or order. If the set already exists in a particular order, then permutation achieves the task of rearranging all of its elements. Mathematically it is represented as:
Combinations refer to the number of ways in which a set of items are selected from a given group of objects such that the order of selecting those items stands invalidated.
Mathematically it is represented as:
Tips for Solving Permutations and Combinations Questions For GATE ECE
The following set of pointers comes in handy while attempting any permutations and combinations online test or any permutations and combinations online quiz out there:
- Make use of permutations if the problem statement requires you to find out the total number of arrangements of objects and count the different orders that are possible in that arrangement.
- Make use of combinations if the problem statement requires you to find the total number of ways a set of objects can be selected without taking the order of selection into account whatsoever.
- Be conversant with both the basic formulae.
- Try and adopt multiple methods while solving problems to arrive at a solution that takes the least time.
Importance of Permutations and Combinations in GATE ECE Exam
Permutations and combinations for GATE ECE should be given proper attention, for it holds the following importance in GATE:
- A basic understanding of the concepts helps you solve a wide array of questions that concern themselves with the fundamental counting principle.
- Familiarity with permutations and combinations helps you efficiently solve problems in probability, a field that is often intertwined with combinatorics.
- Regular practice strengthens your logical and counting abilities, improving your problem-solving skills in general.
- It helps you perform well in the fields of mathematical reasoning and pattern observation and recognition.
Most Recommended Permutations and Combinations Books for GATE ECE
The following permutations and combinations books cover all the topics that are a part of the permutations and combinations syllabus for GATE. They serve as the perfect study material for preparing permutations and combinations GATE notes for the exam.
Quantitative Aptitude for Competitive Examinations
R. S Agarwal (S. Chand Publication)
Fast Track Objective Arithmetic
Magical Book on Quicker Mathematics
M Tyra (BSC Publication)
Sarvesh Kumar Verma
Why Prepare Permutations and Combinations from BYJU'S Exam Prep?
Gradeup’s comprehensive bank of permutations and combinations notes for GATE PDF coupled with its permutations and combinations questions and answers PDF helps candidates gain an in-depth understanding of all the various concepts under this particular topic. Irrespective of whether a candidate is looking for permutations and combinations notes for GATE ECE or permutations and combinations study material for GATE ECE, Gradeup acts as a one-stop solution and furnishes them with additional practice material with its permutations and combinations MCQ PDF.
Q. What do you mean by permutations and combinations?
Permutations refer to actions of arranging certain sets of objects in order. Combinations refer to the act of selecting items from a certain set of objects in such a manner that the order doesn’t matter.
Q. What are some examples of permutations and combinations?
The different ways in which the alphabets A, B, and C can be grouped together, taken all at a time, is an example of permutation. Picking a team of 3 people from a group of 10 people is an example of combination.
Q. What is the formula for permutation?
The formula for permutation is npr=(n!)/(n-r)!
Q. What is the formula for combination?
The formula for Combination is nCr=(n!)/r!(n-r)
Q. What is the relation between permutation and combination?
The relation between permutation and combination is as follows: "nCr= npr /r!"