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 !!

**In a exam paper 1**^{st}section contains 10 questions each with 5 choices and second section contains 5 questions each with 4 choices. In how many different ways can the paper be answered if all the questions are attempted.

A.10^{5 }× 4^{5}

B.5^{10 }× 4^{5}

C.5^{10 }× 5^{4}

D.10^{5 }× 5^{4}

E.None of theseAnswer –**B. 5**^{10 }× 4^{5}

**Explanation :**

10 questions with 5 choices = 5^{10}

20 questions with 4 choices = 4^{5}**How many four digit number can be formed with the digits 5,9,1 and 3 only ?**

A.64

B.216

C.256

D.324

E.None of theseAnswer –**C.256**

**Explanation :**

4*4*4*4 = 256**Find the number of ways in which 9 students equally divided into three groups ?**

A.280

B.360

C.200

D.540

E.None of theseAnswer –**A.280**

**Explanation :**

9!/[3! ×(3!)^{3}] = 362880/6*216 = 280**Find the number of ways of distributing 9 identical balls into 4 boxes so that no box is empty and each box being large enough to accommodate all balls ?**

A.63

B.45

C.62

D.56

E.None of theseAnswer –**D.56**

**Explanation :**

^{9-1}C_{4-1 }=^{8}C_{3 }= 8*7*6/3*2*1 = 56**12 students participated in the competition and each get different score. In how many ways can three different prizes given ?**

A.1320

B.1240

C.1650

D.1870

E.None of theseAnswer –**A.1320**

**Explanation :**

12*11*10 = 1320**How many arrangement can be made from the word COMMERCE, such that all the vowels do not come together ?**

A.6800

B.5600

C.1080

D.9000

E.None of theseAnswer –**D.9000**

**Explanation :**

8 letters = 8!/ 2! 2! = 40320/4 = 10080

6 letters = 6!/2! = 360

Vowels = 3!/2! = 3

No of ways vowels together = 360*3 = 1080

No of ways vowels not together = 10080 – 1080 = 9000**Three brothers have 5 shirts, 8 pants and 6 ties. In how many ways can they wear them ?**

A.2400200

B.2419000

C.2419200

D.2419100

E.None of theseAnswer –**C. 2419200**

**Explanation :**

^{5}P_{3 }*^{8}P_{3}*^{6}P_{3 }= 60*336*120 = 2419200**5 men and 3 women are to be seated such that no 2 women sit together and 2 men sit together. Find the no of ways in which this can be arranged ?**

A.625

B.720

C.525

D.516

E.None of theseAnswer –**B.720**

**Explanation :**

5!*3! = 120*6 = 720**A group consists of 3 couples in which each of the 3 men have one wife each. In how many ways could they arranged in a straight line so that the men and women occupy alternate position ?**

A.216

B.125

C.256

D.72

E.None of theseAnswer –**D.72**

**Explanation :**

3!*3! + 3!*3! = 36+36 = 72**In how many ways can 5 different balls be distributed to 4 different boxes, when each of the can hold any no of ball ?**

A.1024

B.1200

C.1234

D.1600

E.None of theseAnswer –**A.1024**

**Explanation :**

No of way =4^{5 }= 1024

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