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**Permutations and Combinations**

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Question 1 |

**In how many different ways can the letters of the word ‘PRAISE’ be arranged?**

720 | |

610 | |

360 | |

210 | |

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?**

360 | |

240 | |

720 | |

120 | |

None of these |

Question 3 |

**In how many different ways can the letters of the word ‘READERS’ can be**

**arranged?**

1260 | |

2520 | |

5040 | |

720 | |

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?**

50400 | |

4840 | |

3260 | |

2880 | |

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?**

720 | |

684 | |

576 | |

144 | |

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 = 144So 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?**

144 | |

24 | |

6 | |

20 | |

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 lettersThe 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.**

49 | |

1440 | |

7 | |

1898 | |

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?**

56 | |

27 | |

26 | |

41 | |

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?**

12 | |

13 | |

24 | |

52 | |

None of these |

Question 10 |

**The committee should have 2 trainees and 3 research associates?**

15 | |

45 | |

60 | |

9 | |

None of these |

Question 11 |

**Directions (Q. 11-12)**

**:**Study the following information carefully to answer thequestions 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?**

126 | |

45 | |

120 | |

24 | |

None of these |

Question 12 |

**The committee should consist of 2 students, 2 teachers and 1 sports coach?**

25 | |

64 | |

9 | |

36 | |

None of these |

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