Quantitative Aptitude

Permutation and Combination

609 Questions
All Vowels or Objects Together 139 Restricted Group Selection 135 Objects Never Together 98 Fundamental Counting Principle 96 Objects with Repetitions Arrangement 72 Rank or Dictionary Word 20 Selection With Identical Items 15 Pairing or Grouping 10 Distributing Distinct Objects 9 Distributing Identical Objects 9 Circular Ring Arrangement 5 Circular Necklace Arrangement 1

Permutation and Combination Questions

Multiple choice

The number of ways in which Aman, Anaya, Danish and Nero can stand in a straight line such that, Danish comes between Aman and Anaya and Nero does not come between Aman and Anaya is _________________.

  1. 4

  2. 6

  3. 8

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total permutations of 4 people is 4! = 24. Danish between Aman and Anaya: (A, D, An) or (An, D, A). There are 2 arrangements for the trio, and Nero can be in 2 positions (before or after the trio). Total = 2 * 2 = 4.

Multiple choice

Daisy is playing with her friend. They are playing with cards that bear letters of the English alphabet up to L. They want to make a two-letter word (with or without meaning) such that the letter at the first place is a vowel and the letter at the second place is a consonant from A to L. Which of the following can give the maximum number of ways to make such a two-letter word?

  1. 22

  2. 27

  3. 32

  4. 38

  5. 42
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Letters A to L: A, B, C, D, E, F, G, H, I, J, K, L. Vowels: A, E, I (3). Consonants: B, C, D, F, G, H, J, K, L (9). Two-letter word: Vowel then Consonant. Number of ways = 3 * 9 = 27.

Multiple choice

Mr. Wills goes to a famous buffet restaurant, which serves 10 non-vegetarian dishes and 8 vegetarian dishes. If Mr. Wills wants to select 3 non-vegetarian dishes and 2 vegetarian dishes for his brunch, how many different possible combinations of dishes can he choose for his brunch?

  1. 3,360

  2. 3,240

  3. 3,150

  4. 2,860

  5. 2,580
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number of ways to choose 3 non-veg dishes from 10 is 10C3 = 120. The number of ways to choose 2 veg dishes from 8 is 8C2 = 28. Total combinations = 120 * 28 = 3,360.

Multiple choice

Ellie is playing with cards that have letters written on them from A to Z. She wants to form a three-letter word, with or without meaning, with some conditions. She wants the first letter of the word to be M or J, the second letter a vowel, and the third letter from Q to W but not a vowel. How many possible ways are there in which Ellie could form such a word?

  1. 50

  2. 54

  3. 60

  4. 66

  5. 72
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First letter: M or J (2 choices). Second letter: Vowel (A, E, I, O, U - 5 choices). Third letter: Q to W (Q, R, S, T, U, V, W) excluding vowels. Vowels in that range: U. So, Q, R, S, T, V, W (6 choices). Total = 2 * 5 * 6 = 60.

Multiple choice

How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?

  1. 240

  2. 200

  3. 150

  4. 120

  5. N.A
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

LUCKNOW has 7 letters: L, U, C, K, N, O, W. Vowels are U, O (2). Consonants are L, C, K, N, W (5). To pick 4 letters with 2 vowels: Choose 2 vowels (2C2 = 1) and 2 consonants (5C2 = 10). Total sets = 10. Each set has 4! = 24 arrangements. 10 * 24 = 240.

Multiple choice

If the letters in the word 'SEDIMANTATION' are rearranged as they appear in the English alphabet, then the position of how many letters will remain unchanged after the rearrangement?

  1. 0

  2. 1

  3. 2

  4. 3

  5. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

SEDIMANTATION (13 letters): A, A, D, E, I, I, M, N, N, S, T, T. Alphabetical: A, A, D, E, I, I, M, N, N, S, T, T. Comparing original to sorted: S-A, E-A, D-D (match), I-E, M-I, A-I, N-M, T-N, A-N, T-S, I-T, O-T, N-T. Only 'D' remains in the same position.

Multiple choice

Given below are two statements: Statement I: A committee of 4 can be made out of 5 men and 3 women containing at least one woman in 65 ways. Statement II: The number of words which can be formed using letters of the word ARRANGE so that vowels always occupy even place is 36. In light of the above statements, choose the correct answer from the options given below.

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: Total ways to choose 4 from 8 is 8C4 = 70. Ways with no women (choosing 4 from 5 men) is 5C4 = 5. Ways with at least one woman = 70 - 5 = 65. True. Statement II: ARRANGE has 7 letters (A:2, R:2, N:1, G:1, E:1). Vowels are A, A, E (3). Even positions are 2, 4, 6 (3). We place 3 vowels in 3 spots: 3! / 2! = 3 ways. Remaining 4 letters (R, R, N, G) in 4 spots: 4! / 2! = 12 ways. Total = 3 * 12 = 36. True.