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 how many ways can 3 prizes be given away to 12 students when each student is eligible for all the prizes ?**

A.1234

B.1728

C.5314

D.1331

E.None of these

Answer –**B.1728**

**Explanation :**

12^3 = 1728

**Total no of ways in which 30 sweets can be distributed among 6 persons ?**

A.35 C_{5}

B.36 C_{5}

C.36 C_{6}

D.35!/5!

E.None of these

Answer –**A.**^{ 35 }C_{5}

**Explanation :**

^{30+6-1 }C_{6-1}=^{35 }C_{5}

**A bag contains 4 red balls and 5 black balls. In how many ways can i make a selection so as to take atleast 1 red ball and 1 black ball ?**

A.564

B.345

C.465

D.240

E.None of these

Answer –**C.465**

**Explanation :**

2^{4}-1 = 16 -1 = 15

2^{5-}1 = 32 -1 = 31

15*31 = 465

**In how many ways can 7 beads be strung into necklace ?**

A.2520

B.5040

C.720

D.360

E.None of these

Answer –**D.360**

**Explanation :**

No of way in Necklace = (n-1)!/2 = 6!/2

= 720/2 = 360

**Find the no of 3 digit numbers such that atleast one of the digit is 6 (with repetitions) ?**

A.252

B.345

C.648

D.560

E.None of these

Answer –**A.252**

**Explanation :**

Total no of 3 digit number = 9*10*10 = 900

No of 3 digit number- none of the digit is 6 = 8*9*9 = 648

No of 3 digit number – atleast one digit is 6 = 900-648 = 252

**In how many ways can 7 girls and 4 boys stand in a row so that no 2 boys are together ?**

A.8467200

B.9062700

C.7407000

D.8407200

E.None of these

Answer –**A. 8467200**

**Explanation :**

No of ways = 7!*^{8}P_{4}

7! = 5040

8P4 = 8*7*6*5 = 1680

No of ways = 5040*1680 = 8467200

**In how many ways the letters of the word PERMUTATION be arranged ?**

A.10!/2!

B.10!

C.11!

D.11!/2!

E.None of these

Answer –**D. 11!/2!**

**Explanation :**

No of ways = 11!/2!

**How many numbers can be formed with the digits 1, 7, 2, 5 without repetition ?**

A.89

B.56

C.64

D.72

E.None of these

Answer –**C.64**

**Explanation :**

1 digit number = 4

2 digit no = 4*3 = 12

3 digit no = 4*3*2 = 24

4 digit no = 4*3*2*1 = 24

Total = 4+12+24+24 = 64

**There are 3 boxes and 6 balls. In how many ways these balls can be distributed if all the balls and all the boxes are different?**

A.243

B.512

C.729

D.416

E.None of these

Answer –**C.729**

**Explanation :**3^6 = 729

**In how many ways can 4 books be selected out of 10 books on different subjects ?**

A.210

B.320

C.716

D.5040

E.None of these

Answer –**A.210**

**Explanation :**

^{16}C_{4 }= 10*9*8*7/4*3*2*1 = 5040/24 = 210

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