### Quantitative Aptitude

## PERMUTATION AND COMBINATION MCQs

### Total Questions : 100

**Page 1 of 5 pages**

**There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card?**

__Question 6.__- 210
- 210 × 33
- 4 × 34
- 42 × 33

**Answer: Option C**

**From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?**

__Question 7.__- 138
- 128
- 112
- 91

**Answer: Option D**

**Jay wants to buy a total of 100 plants using exactly a sum of Rs. 1000. He can buy Rose plants at Rs. 20 per plant or marigold or Sun flower plants at Rs. 5 and Rs. 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?**

__Question 10.__- 2
- 3
- 4
- 5
- None of these

**Answer: Option B**

**There are 20 couples in a party. Every person greets every person except his or her spouse. People of the same sex shake hands and those of opposite sex greet each other with a Namaste (It means bringing one's own palms together and raising them to the chest level). What is the total number of handshakes and Namaste's in the party?**

__Question 14.__- 760
- 1140
- 780
- 720

**Answer: Option B**

**In a certain laboratory, chemicals are identified by a colour-coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two-colour pair. If the order of colours in the pairs does not matter, what is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours?**

__Question 15.__- 7
- 6
- 5
- 8

**Answer: Option B**

**Six boxes are numbered 1, 2, 3, 4, 5 and 6. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. find the total number of ways of placing the balls.**

__Question 16.__- 15
- 20
- 21
- 36

**Answer: Option C**

### Are Permutations Or Combinations Bigger?

There are always more permutations than combinations since permutations are ordered combinations. Take any combination and line them up in different ways and we have different permutations. In your example there are 10C4 = 210 combinations of size 4 but 4! = 24 times as many permutations.

### How Do You Create A Permutation?

If n is odd, swap the first and last element and if n is even, then swap the ith element (i is the counter starting from 0) and the last element and repeat the above algorithm till i is less than n. In each iteration, the algorithm will produce all the permutations that end with the current last element.

### How Do You Know If A Word Is A Permutation Or Combination?

Always keep an eye on the keywords used in the question. The keywords can help you get the answer easily. The keywords like-selection, choose, pick, and combination-indicates that it is a combination question. Keywords like-arrangement, ordered, unique- indicates that it is a permutation question.

### How Do You Make A Combination?

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.

### How Do You Make Permutations Strong And Combination?

How to improve in Permutation and Combination:

- You should be clear with all the basic formulas.
- There are some typical questions from this area which you should be aware of.
- While practicing, try solving questions with more than one method and then see which of the method takes the least time.

### How Do You Solve Permutations And Combinations Easily?

Combination Formula,

nCr = (nr) = nPr / r! = n! / {r! (n-r)!} These are the key formulas to find out probability permutations and combinations.

### How Many Types Of Permutations Are There?

There are basically two types of permutation: Repetition is Allowed: such as the lock above. It could be "333". No Repetition: for example the first three people in a running race.

### What Are The Similarities Between Permutations And Combinations?

In terms of mathematical concepts, “Permutation” and “Combination” are related to each other. Combination is the counting of selections that we make from n objects. Whereas Permutation is counting the number of arrangements from n objects.

### What Is N And R In Permutation?

n refers to the number of objects from which the permutation is formed; and r refers to the number of objects used to form the permutation.

### What Is An Example Of Permutations And Combinations?

Give examples of permutations and combinations:

An example of permutations is the number of 2 letter words that can be formed by using the letters in a word say, GREAT; 5P_2 = 5!/(5-2)! An example of combinations is in how many combinations we can write the words using the vowels of the word GREAT; 5C_2 =5!/[2! (5-2)!]

### What Is Difference Between Permutation And Combination?

A permutation is a method of arranging all the members in order. The combination is selection of elements from a collection.

### What Is Permutation And Combinations?

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

### What Is The Application Of Permutation And Combination?

Permutations are used when order/sequence of arrangement is needed. Combinations are used when only the number of possible groups are to be found, and the order/sequence of arrangements is not needed. Permutations are used for things of a different kind. Combinations are used for things of a similar kind.

### How Many Permutations Does 1234 Have?

There are 24 permutations. The 12 even permutations are: id , (1 2 3 4) , (1 3 2 4) , (1 4 2 3) , (1 2 3) , (1 2 4) , (1 3 2) , (1 3 4) , (1 4 2) , (1 4 3) , (2 3 4) , (2 4 3).

### Is A Password A Permutation Or Combination?

Another example of a permutation we encounter in our everyday lives is a passcode or password. To unlock a phone using a passcode, it is necessary to enter the exact combination of letters, numbers, symbols, etc., in an exact order. In cases where the order doesn't matter, we call it a combination instead.

### What Are The Concepts Of Combination?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.

### What Is The Relationship Between Permutation And Combination?

In terms of mathematical concepts, “Permutation” and “Combination” are related to each other. Combination is the counting of selections that we make from n objects. Whereas Permutation is counting the number of arrangements from n objects.

### What Is The Similarities Between Permutation And Combination?

Permutations and combinations are both related mathematical concepts. Because they are related concepts, most of the time they are used with each other or switched or swapped with each other without realizing it.

### Which Has More Outcomes Permutation Or Combination?

There are always more permutations than combinations since permutations are ordered combinations. Take any combination and line them up in different ways and we have different permutations.

### Why Permutation And Combination Is Important?

Permutation is used when the objects and things are of different kinds. The smaller groups that can be formed from the elements of a larger group is Combination. When we need to arrange a sequence of things, we need Permutations whereas in order to find how many possible groups can be formed , we need Combinations.

### Where Is Permutation Used?

Permutations are used in almost every branch of mathematics, and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences.

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