# Permutations and Combinations Questions Answers Online Test MCQ

Permutations and Combinations Questions Answers Online Test MCQ. Permutations and Combinations Problem comes under Aptitude: This mock test having 15 question, with four choices. On each click on answers system will tell you where the answers is correct or incorrect. You can view this Permutations and Combinations test question details at the end of the quiz.

## Permutations and Combinations Questions Answers

This Permutations and Combinations questions answers are applicable for any kind of entrance exam or job related exam especially for bank exams, GMAT, CAT, SBI PO practice as much as you can so gather knowledge of how to answers Permutations and Combinations critical in short time and this can be a big factor for cracking any exam.

## Permutations and Combinations

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 Question 1
In how many different ways can the letters of the word ‘PRAISE’ be arranged?
 A 720 B 610 C 360 D 210 E None of these
Question 1 Explanation:
The word ‘PRAISE’ has six different letters P, R, A, I, S and E i.e. n = 6 The six different letters can be arranged in 6! = 720 ways
 Question 2
In how many different ways can the letters of the word ‘STRESS’ be arranged?
 A 360 B 240 C 720 D 120 E None of these
 Question 3
In how many different ways can the letters of the word ‘READERS’ can be arranged?
 A 1260 B 2520 C 5040 D 720 E None of these
 Question 4
In how many different ways can the letters of the word ‘PREVIOUS’ be arranged in such a way that the vowels always come together?
 A 50400 B 4840 C 3260 D 2880 E 2420
Question 4 Explanation:
Treating the group of four vowels (E, I O and U) as one distinct letter then total number of letters will be 8 - 4 + 1 = 5 [i.e. P, R, V, S and (E, I, O, U)] The five letters can be arranged in 5! = 120 ways The vowels among themselves can be arranged in 4! = 24 ways The letters of the word ‘PREVIOUS’ can be arranged in 120 × 24 = 2880 ways such that vowels always come together.
 Question 5
In how many different ways can the letters of the word ‘REASON’ be arranged in such a way that all the vowels will never come together?
 A 720 B 684 C 576 D 144 E None of these
Question 5 Explanation:
The letters of the word ‘REASON’ can be arranged in 6! = 720 ways Number of ways that the letters can be arranged such that all vowels come together = 4! × 3! = 24 × 6 = 144 So number of arrangements in which all the vowels will not come together = 720 – 144 = 576
 Question 6
How many words can be formed out of the letters of the word ‘ARTICLE’ so that the vowels occupy the even places?
 A 144 B 24 C 6 D 20 E 60
Question 6 Explanation:
The word ‘ARTICLE’ has Seven letters. So it contains seven places (3 even and 4 odd) to be filled with the letters The three vowels can be placed in 3 even places in 3! = 6 ways The four consonants can be placed in 4 odd places in 4! = 24 ways Seven letters can be placed in seven places in which vowels take only even positions = 6 × 24 = 144 ways
 Question 7
The letters of the word PROMISE are arranged so that no two of the vowels should come together. Find the total number of arrangements.
 A 49 B 1440 C 7 D 1898 E None of these
Question 7 Explanation:
The consonants of the word ‘PROMISE’ (P, R, M and S) can be first arranged in 4! =24 ways The vowels of the word ‘PROMISE’ (O, I and E) then can be placed in between two consonants including the first and the last positions. Then five places will be available to place vowels. The three vowels can be placed in 5 positions in 5 P 3 = 5 × 4 × 3 = 60 ways The required number of arrangements = 24 × 60 = 1440
 Question 8
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed?
 A 56 B 27 C 26 D 41 E None of these
 Question 9
Directions (Q. 9-10): Study the given information carefully and answer the questions that follow: A committee of five members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done if —   The committee should have all 4 professors and 1 research associate or all 3 trainees and 2 professors?
 A 12 B 13 C 24 D 52 E None of these
 Question 10
The committee should have 2 trainees and 3 research associates?
 A 15 B 45 C 60 D 9 E None of these
 Question 11
Directions (Q. 11-12): Study the following information carefully to answer the questions that follow: A committee of five members is to be formed out of 4 students, 3 teachers and 2 sports coaches. In how many ways can the committee be formed if 12. Any five people can be selected?
 A 126 B 45 C 120 D 24 E None of these
 Question 12
The committee should consist of 2 students, 2 teachers and 1 sports coach?
 A 25 B 64 C 9 D 36 E None of these
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