Permutation and Combination Questions with Answers PDFs for MBA Preparation

As per the definition, the counting rule or the fundamental counting principle states that if an event has p outcomes and another event has q outcomes, then the number of outcomes when both these events occur together is p x q.

Permutation Formula:

ⁿP_r = (n!) / (n-r)!

Combination Formula:

ⁿC_r = n!/r!(

A Permutation is an arrangement in a particular order of several things considered a few or all at a time.

Theorem 1: The number of permutations of k different objects taken l at a time, where 0 ^kP_l

Theorem 2: The number of permutations of k different objects taken l at a time, where repetition is allowed, is k^r.

Theorem 3: The number of permutations of k objects, where l objects are of the same kind and the rest is all different is k!/l!

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A Combination refers to the number of possible arrangements possible for an event. In combination, the order of selection does not matter.

The number of combinations of k items taken at a time is denoted as ^kC_l.

Theorem 4: ^kC_k-l = k!/(k-l)!(k- (k-l))! = k!/(k-l)! l!= ^kC_l

We infer that, selecting l items from k items also means rejecting k-l items.

Theorem 5: ^kC_l = ^kC^m ⇒ l = m or l = k-m, i.e., k = l + m

Theorem 6: ^kC_l = ^kC_l-1 = ^k+1C_l

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Illustrated Examples of Permuation-Combination

Q 1: Find the value of k such that, ^kP₅ = 42 ^kP₃ , k>4

Solution:

Given that, ^kP₅ = 42 ^kP₃

Applying the formula of permutation,

k (k – 1) (k – 2) (k – 3) (k– 4) = 42 k(k – 1) (k– 2) 

According to the question, k > 4 so k(k – 1) (k – 2) ≠ 0

Therefore, by dividing both sides by k(k – 1) (k – 2), we get

(k – 3 (k – 4) = 42 or k2 – 7k – 30 = 0 

or k2 – 10k + 3k – 30 or (k – 10) (k + 3) = 0 

or k – 10 = 0 or k + 3 = 0 or k = 10  or k = – 3

As k cannot be negative, so k= 10.

Q 2: If ^kC₉ = ^kC₈, find ^kC₁₇ ?

Solution:

Given, ^kC₉ = ^kC₈

k!/9!(k-9)!= k!/8! (k-8)!

That is, 1/9= 1/k-8

So, k-8 = 9

Hence, k=17 and ^kC₁₇ = ¹⁷C₁₇ = 1

Q 3: In how many ways can 5 balls and 3 boxes be arranged in a row so that no two boxes are together?

Solution:

The 5 balls can be arranged in 5! ways, and to ensure that no two boxes are together, 3 boxes can be put in ⁶C₃ ways.

Total = 5! X  ⁶C₃ = 5! X 6!/3!= 4x 5x 2x 3x 4x 5x 6 = 14,400 ways

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• Mean, Mode, Median
• Square Root and Cube Root

Quantitative Aptitude Questions with Answers for Practice

Quant Easy Test	Quant Easy Test Solution
Quant-Medium Test	Quant Medium Test Solutions
Quant Difficult Test	Quant Difficult Test Solution

In order to further simplify this concept, we have shared key differences between Permutation and Combination. This table will help you in conceptual clarity.

Particulars	Permutation	Combination
Definition	Permutation is an arrangement of all members in a particular order.	A combination is a selection of members from a collection or group.
Represents	Arrangement	Selection
Order	Values are arranged in a specific order.	Values are not arranged in any specific order.
Derivation	There can be multiple permutations from a single combination.	There can be only single combination from a single permutation.
Formula	nPr = n!/(n-r)!	nCr = n!/(r!)(n-r)!

Read more: Difference between Permutation and Combination

Practice of sample questions plays a very important role in Quants preparation. Get here sample questions and practice tests of how to prepare for Quantitative Aptitude for CAT pdf with solutions for practice. 

CAT Quant_Easy-Test_1_Questions	CAT Quant_Easy Test 1_Solutions
CAT Quant_Medium_Test_1_Questions	CAT Quant_Medium_ Test 1_Solutions
CAT Quant_Difficult_Test_1_Questions	CAT Quant_Difficult_Test 1_Solutions

CAT Quant_Easy Test 2 Questions	CAT Quant_Easy Test 2 Solutions
CAT Quant_Medium Test 2 Questions	CAT Quant_Medium Test 2 Solutions
CAT Quant_Difficult Tes 2 Questions	CAT Quant_Difficult Test 2 Solutions

CAT_Quant_Easy_Test-_Set_3	CAT_Quant_Easy_Test_-_Set_3_Solutions
CAT_Quant_Medium_Test_-_Set_3	CAT_Quant_Medium__Test_Set_3_Solutions
CAT_Quant_Difficult_Test_-_Set_3	CAT_Quant_Difficult_Test_-_Set_3_Solutions

CAT_Quant_Easy_Test_Set_4	CAT_Quant_Easy_Test_Set_4_Solutions
CAT_Quant_Medium_Test_Set_4	CAT_Quant_Medium_Test_Set_4_Solutions
CAT_Quant_Difficult_Test_Set_4	CAT_Quant_Difficult_Test_Set_4_-Solutions

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