91�ȱ� Style Quiz - Permutations & Combinations

vishnuprasad.kesavamoorthy@vepl.com — Thu, 09 Mar 2017 08:43:43 +0000

Quiz Topic: P&C

Question:

Question content:

In a class of 15 boys and 10 girls, the class teacher wants to select one class representative and one cultural representative.

In how many ways it can be done so that the class representative is a boy and the cultural representative is a girl?

Option 1:

120

Option 2:

Option 3:

300

Option 4:

150

Option 5:

172

Correct options: 4

Explanation:

Since this can also be a numeric entry question and you may not have options to choose from, it is paramount that you understand the concept behind this problem. So, when you see the word ‘select’, you must keep in mind to use ‘Combination’ to solve this question.

Now, we know that out of 15 boys and 10 girls, there must be one class representative who’s a boy and one cultural representative who’s a girl.
Therefore, the number of ways in which you can select a class representative = 15
Similarly, the number of ways in which you can select a cultural representative = 10.

Now, the question requires you to find the number of ways you can select a class representative who’s a boy AND a cultural representative who’s a girl.
Therefore, the total number of ways = 15 x 10 = 150 ways.

More Explanation:

If you used ²⁵C₂ to calculate the answer, then you’ll actually only select any two students - not necessarily a boy and a girl.

If you answered with 25, then it denotes the number of ways by which you can either select on class representative or a cultural representative.
If you have any further doubts, do click on the ‘Ask a Doubt’ option and we’ll be happy to clarify it for you!
Good luck! Try the next question!

Question content:

Quantity A: Number of two-digit even integers with the tens digit not equal to the units digit.
Quantity B: 45

Which of the following is/are true?

Option 1:

Quantity A is greater

Option 2:

Quantity B is greater

Option 3:

The two quantities are equal

Option 4:

The relationship cannot be determined from the information given

Correct options: 1

Explanation:

Since this question requires us to use permutation, let us use the concept of visualization to help us here.
Let the number be represented as:
_ _

It is very clear that Quantity A is a two digit even number.
Therefore, the units place can be either 0, 2, 4, 6, or 8. Hence, there are 5 ways to fill the units place.
i.e. _ 5

Coming to the tens digit, we can have any number except for the digit 0 and the number in the unit’s place.
Therefore, there are 8 ways to fill the tens digit.
i.e. 8 5

So, number of two digit even numbers = 8 x 5 = 40.
Now, since the question states two digit even integers, it can include both positive and negative numbers.
Therefore, total number of two digit even integers are 40 + 40 = 80.

From the question, we know Quantity B is 45.
Therefore, Quantity A is greater. The correct answer is Option A.

More Explanation:

If you had chosen option B as your answer, then you might have considered only the positive integers i.e. 40.
If you had chosen option C, then you might have considered only the number of “positive integers” and assumed that there are 9 ways to fill the tens place.
Good Luck!

Submit BB Id: 183

Quiz Name: 91�ȱ� Style Quiz - Permutations & Combinations

Basic Quiz – Permutations & Combinations

vishnuprasad.kesavamoorthy@vepl.com — Wed, 08 Mar 2017 13:43:31 +0000

Difficulty Level: Basic

Quiz Topic: P&C

Question:

Question content:

In how many ways can the letters of the word
'VERBAL'
be rearranged?

Option 1:

Option 2:

Option 3:

720

Option 4:

188

Option 5:

192

Correct options: 3

Explanation:

The best way to solve questions related to Permutations and Combinations is to use the concept of Visualization.
Since, the word VERBAL has six letters, draw 6 blanks on your rough sheet.
_ _ _ _ _ _
Since the question asked for how many ways it can be rearranged, you must use Permutations. So, since there are totally 6 letters, the first blank can take all of the 6 letters.

Therefore, the first blank can be filled in 6 ways.6 _ _ _ _ _
Now, once a letter is used up for a blank, it cannot be repeated. Therefore, the second blank can take only 5 letters. 6 x 5 _ _ _ _

Similarly, the subsequent blanks can be filled one after another.
6 x 5 x 4 x 3 x 2 x 1 = 720 ways.

Many students tend to immediately calculate the answer as 6 x 6 = 36 ways.
However, this will only give you the ways in which you can form any 6 letter word (with or without meaning) using the letters of Verbal.

If you any doubt, click on ‘Ask A Doubt’ and we’ll reply back with an answer!
Good Luck! Try the next questions!

Question content:

2. There are 2 multiple choice questions with 5 options.

If there is only one correct answer, in how many ways can a student answer the questions correctly?

Option 1:

Option 2:

Option 3:

Option 4:

Option 5:

Correct options: 4

Explanation:

This can also come as a numeric entry question which doesn’t have any answer options for you to choose from. So, intelligent guessing will not work here.

The best technique is to visualize the question from what is given.
Q1 → 5 options → 1 correct answer
Q2 → 5 options → 1 correct answer
Since the question asks for the number of ways in which both questions can be answered correctly, you must calculate the answer like this:

Number of ways in which you can get the first question correct = 1 (only one correct answer)
Number of ways in which you can get the second question correct = 1 (only one correct answer)

Therefore, number of ways to answer question 1 AND 2 correctly = 1 + 1 = 2
Hence, the correct answer is 2.

If you got answers like:

Option A: 1
Remember, that the question asks for you to solve not just one but both questions correctly. Therefore, you must get question 1 & 2 right, which means 1 + 1 = 2. If the question asks for question 1 OR question 2, then you can calculate as 1 x 1 = 1.

Option D:10
If you had chosen this answer, it is possible that you may have confused the number of ways to answer a question with the number of ways to CORRECTLY answer a question.
The number of ways to answer a multiple choice question = 5
However, the number of correct answers is only 1.

Submit BB Id: 183

Quiz Name: Basic Quiz – Permutations & Combinations

91�ȱ� - P&C

91�ȱ� Style Quiz - Permutations & Combinations

Basic Quiz – Permutations & Combinations