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 5 rings can be worn on 3 fingers?**

A) 15

B) 120

C) 60

D) 70

E) 243**C) 60**

Explanation:

0 0 0

Let these 3 circles are 3 fingers

For 1st finger we have 5 choices, for second finger we have 4 choices left of rings, for third finger we have 3 choices left.

So total 5*4*3 = 60 ways**In how many ways the letters of the word ‘AUTHOR’ be arranged taking all the letters?**

A) 120

B) 720

C) 360

D) 60

E) None of these**B) 720**

Explanation:

AUTHOR contains 6 letters, so total 6! ways.**In how many ways the letters of the word ‘MINIMUM’ be arranged taking all the letters?**

A) 420

B) 840

C) 5040

D) 720

E) 360**A) 420**

Explanation:

MINIMUM contains 7 letters, so total 7! ways. But it contains 2 I’s and 3 M’s so divide by 2! And 3!

So ways 7!/(2! * 3!) = 7*6*5*4*3*2*1 / 2*1*3*2*1 = 420**How many words of 4 letters with or without meaning be made from the letters of the word ‘LEADING’, when repetition of letters is allowed?**

A) 4808

B) 57600

C) 2401

D) 57624

E) None of these**D) 57624**

Explanation:

LEADING is 7 letters.

We have 4 places where letters are to be placed.

For first letter there are 7 choices, since repetition is allowed, for second, third and fourth letter also we have 7 choices each, so total of 7*7*7*7 ways = 2401 ways.

Now for arrangement of these 4 words, we have 4! Ways.

So total of 2401 * 4! Ways.**In how many ways letters of word ‘INVISIBLE’ be arranged such that all vowels are together?**

A) 2560

B) 2880

C) 5040

D) 2520

E) 720**B) 2880**

Explanation:

First make IIIE in a circle. So we have

Now we have N, V, S, B, L and box, their arrangements can be done in 6!

Letters inside circle are also to be arranged, we have I, I, I, E so ways are 4!/3!

Total ways 6! * 4!/3!**How many words can be made out of the letters of word ‘POUNDING’ such that all vowels occupy odd places?**

A) 1440

B) 1400

C) 7200

D) 5600

E) 40320**A) 1440**

Explanation:

In POUNDING, there are 8 places

1 2 3 4 5 6 7 8

So for 3 places selection of vowels, we have 1, 3, 5, 7 number places^{4}C_{3}ways

Now for arranging these 3 vowels, ways are 3!

Remaining 5 are consonants (in which there are 2 N’s) for which 5!/2!

so total ways =^{4}C_{3}*3!*(5!/2!)**In how many ways a group of 2 men and 4 women be made out of a total of 4 men and 7 women?**

A) 720

B) 210

C) 420

D) 360

E) 120**B) 210**

Explanation:

We have to select 2 men from 4 men, and 4 women from 7 women

So total ways =^{4}C_{2}*^{7}C_{4}**There are 8 men and 7 women. In how many ways a group of 5 people can be made such that at least 3 men are there in the group?**

A) 1545

B) 1626

C) 1722

D) 1768

E) 1844**C) 1722**

Explanation:

Case 1: 3 men and 2 women

^{8}C_{3}*^{7}C_{2}= 1176

Case 2: 4 men and 1 women

^{8}C_{4}*^{7}C_{1}= 490

Case 3: all 5 men

^{8}C_{5}= 56

Add all the cases.**There are 6 men and 7 women. In how many ways a committee of 4 members can be made such that a particular woman is always included.**

A) 180

B) 120

C) 240

D) 220

E) 260**D) 220**

Explanation:

There are total 13 people, a particular woman is to be included, so now 12 people are left to chosen from and 3 members to be chosen. So ways are^{12}C_{3}.**There are 5 men and 3 women. In how many ways a committee of 3 members can be made such that 2 particular men are always to be excluded.**

A) 50

B) 20

C) 24

D) 48

E) None of these**B) 20**

Explanation:

Total 8 people, 2 men are to excluded, so 6 men left to be chosen from and 3 members to be chosen. So ways are^{6}C_{3}.

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