Permutation & Combination Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Permutations & Combination PRACTICE TEST [1 - EXERCISES]

Permutation & Combination Model Questions Set 1

Question : 6

The number of ways in which four letters of the word 'MATHEMATICS' can be arranged is

a) 1680

b) 2454

c) 192

d) 136

e) None of these

Answer: (a)

There are 8 different letters in the word MATHEMATICS;

three letters M, A and T being repeated.

The number of ways in which four letters of the word

MATHEMATICS can be arranged = $^8P_4$

= 8 × 7 ×6 × 5 = 1680

Question : 7

In how many different ways can the letters of the word 'ARMOUR' be arranged?

a) 640

b) 300

c) 350

d) 720

e) None of these

Answer: (e)

ARMOUR = 6 letter whereas R repeated twice

∴ ${6!}/{2!}$ = ${6 × 5 × 4 × 3 × 2 × 1}/{2 × 1}$ = 360

Question : 8

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

a) 30

b) 5 ! × 4 !

c) 7 ! × 5 !

d) 6 ! × 5 !

e) None of these

Answer: (d)

6 men can be sit by 5! ways and on remaining 6 seats, 5 women can sit by $^6C_5$ ways.

∴ Required number of ways = 5! × $^6P_5$ = 6! × 5!

permutation and combinations mcq problems competitive exams 3 8

Question : 9

In how many different ways can the letters of the word "COUNTRY" be arranged in such a way that the vowels always come together?

a) 2880

b) 1440

c) 5040

d) 720

e) None of these

Answer: (b)

There are seven letters in the word "COUNTRY" and two vowels O and U. Considering two vowels as one unit, total number of letters will be 5 + 1 = 6. So, number of arrangements = 6!

Now, the two vowels can be arranged in 21 ways among themselves.

∴ Total number of ways = 6! × 2! = 1440

Question : 10

In how many different ways can hte letters of the word 'PRETTY' be arranged?

a) 360

b) 36

c) 720

d) 120

e) None of these

Answer: (a)

Number of ways = ${6!}/{2!}$ (∵ T letter comes in two time)

= ${6 × 5 × 4 × 3 × 2 × 1}/{2 × 1}$ = 360

IMPORTANT quantitative aptitude EXERCISES

Permutation & Combination Model Questions Set 1 Online Quiz

Click to Start..

Recently Added Subject & Categories For All Competitive Exams

Puzzle Reasoning Questions Answers PDF: IBPS Clerk 2024

Top Reasoning Puzzle Test questions with answers, fully solved explanation and download PDF for IBPS Clerk Prelims 2024. Aptitude MCQ-based practice test

20-May-2024 by Careericons

Continue Reading »

Most Important Antonyms Vocabulary - IBPS Clerk Prelims 2024

Latest Antonyms multiple choice questions and answers with free PDFfor IBPS Clerk Prelims 2024. English Vocabulary practice exercise for all bank exam

17-May-2024 by Careericons

Continue Reading »

Syllogism Practice Questions Answers PDF - IBPS Clerk 2024

Practice Verbal Reasoning Syllogism multiple choice questions and answers with Fully solved explanation, PDF for the IBPS Clerk Prelims 2024 Bank Exam

16-May-2024 by Careericons

Continue Reading »

IBPS Clerk Prelims 2024 Synonyms Questions Solved Answers

Most important IBPS Clerk Prelims 2024 Synonyms and Antonyms multiple choice questions and answers with detailed solutions, English vocabulary PDF Download

14-May-2024 by Careericons

Continue Reading »