Hello Aspirants. Welcome to Online Reasoning Section in AffairsCloud.com. Here we are creating question sample in coded **Permutations & Combinations**, which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

Questions Penned by Yogit

**How many 3 digit number can be formed with the digits 5, 6, 2, 3, 7 and 9 which are divisible by 5 and none of its digit is repeated?**

a) 12

b) 16

c) 20

d) 24

e) None of these

Answer –**c) 20**

**Explanation :**

_ _ 5

first two places can be filled in 5 and 4 ways respectively so, total number of 3 digit number = 5*4*1 = 20

**In how many different ways can the letter of the word ELEPHANT be arranged so that vowels always occur together?**

a) 2060

b) 2160

c) 2260

d) 2360

e) None of these

Answer –**b) 2160**

**Explanation :**

Vowels = E, E and A. They can be arranged in 3!/2! Ways

so total ways = 6!*(3!/2!) = 2160

**There are 4 bananas, 7 apples and 6 mangoes in a fruit basket. In how many ways can a person make a selection of fruits from the basket.**

a) 269

b) 280

c) 279

d) 256

e) None of these

Answer –**c) 279**

**Explanation :**

Zero or more bananas can be selected in 4 + 1 = 5 ways (0 orange, 1 orange, 2 orange, 3 orange and 4 orange)

similarly apples can be selected in 7 +1 = 8 ways

and mangoes in 6 +1 = 7 ways

so total number of ways = 5*8*7 = 280

but we included a case of 0 orange, 0 apple and 0 mangoes, so we have to subtract this, so 280 – 1 = 279 ways

**There are 15 points in a plane out of which 6 are collinear. Find the number of lines that can be formed from 15 points.**

a) 105

b) 90

c) 91

d) 95

e) None of these

Answer –**c) 91**

**Explanation :**

From 15 points number of lines formed = 15c2

6 points are collinear, number of lines formed by these = 6c2

So total lines = 15c2 – 6c2 + 1 = 91

**In how many ways 4 Indians, 5 Africans and 7 Japanese be seated in a row so that all person of same nationality sits together**

a) 4! 5! 7! 3!

b) 4! 5! 7! 5!

c) 4! 6! 7! 3!

d) can’t be determined

e) None of these

Answer –**a) 4! 5! 7! 3!**

**Explanation :**

4 Indians can be seated together in 4! Ways, similarly for Africans and Japanese in 5! and 7! respectively. So total ways = 4! 5! 7! 3!

**In how many ways 5 Americans and 5 Indians be seated along a circular table, so that they are seated in alternative positions**

a) 5! 5!

b) 6! 4!

c) 4! 5!

d) 4! 4!

e) None of these

Answer –**c) 4! 5!**

**Explanation :**

First Indians can be seated along the circular table in 4! Ways and now Americans can be seated in 5! Ways. So 4! 5! Ways

**4 matches are to be played in a chess tournament. In how many ways can result be decided?**

a) 27

b) 9

c) 81

d) 243

e) None of these

Answer –**c) 81**

**Explanation :**

Every chess match can have three result i.e. win, loss and draw

so now of ways = 3*3*3*3 = 81 ways

**Q(8 –9)** There are 6 players in a cricket which is to be sent to Australian tour. The total number of members is 12.

**If 2 particular member is always included**

a) 210

b) 270

c) 310

d) 420

e) None of these

Answer –**a) 210**

**Explanation :**

only 4 players to select, so it can be done in 10c4 = 210

**If 3 particular player is always excluded**

a) 76

b) 82

c) 84

d) 88

e) None of these

Answer –**c) 84**

**Explanation :**

6 players to be selected from remaining 9 players in 9c6 = 84 ways

**In a group of 6 boys and 5 girls, 5 students have to be selected. In how many ways it can be done so that at least 2 boys are included**

a) 1524

b) 1526

c) 1540

d) 1560

e) None of these

Answer –**b) 1526**

**Explanation :**

6c2*5c3 + 6c3*5c2 + 6c4*5c1 + 6c5

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