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 the letters of the word "VALEDICTORY" be arranged so that the vowels may never be separated is
  1. $7! 4!$
  2. $8! 4!$
  3. $7!  ^8P_4 $
  4. $4! 3!$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

VALEDICTORY has 11 letters: V, L, D, C, T, R, Y (7 consonants) and A, E, I, O (4 vowels). Treating the 4 vowels as one block, we have 8 items to arrange (7 consonants + 1 block) in 8! ways. The 4 vowels can be arranged within their block in 4! ways. Total = 8! * 4!.

Multiple choice

How many 6-letter words with distinct letters in each can be formed using the letters of the word EDUCATION? How many of these begin with I
  1. $\displaystyle ^{9}P_{6'}$ $\displaystyle ^{8}P_{5}$
  2. $\displaystyle ^{9}P_{6'}$ $\displaystyle ^{9}P_{5}$
  3. $\displaystyle ^{8}P_{6'}$ $\displaystyle ^{8}P_{5}$
  4. $\displaystyle ^{8}P_{6'}$ $\displaystyle ^{8}P_{4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

EDUCATION contains 9 distinct letters, so the number of six-letter arrangements is 9P6. If the word begins with I, the remaining five positions can be filled from the other 8 letters in 8P5 ways.

Multiple choice

All the six letters of the name SACHIN are arranged to from different words without repeating any letter in any one word.The words so formed are then arranged as in a dictionary. What will be the Position of the world SACHIN in that sequence?
  1. $436$
  2. $590$
  3. $601$
  4. $751$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Alphabetical order: A, C, H, I, N, S. Words starting with A: 5! = 120. C: 120. H: 120. I: 120. N: 120. Total = 600. The next word is SACHIN, which is 601.

Multiple choice

Different words being formed by arranging the letters of the word "INTERMEDIATE". All the words obtained are written in the form of a dictionary, lf vowels & consonants occupy their original places, then the number of permutations is
  1. $\displaystyle \frac{6!}{2!}\times\frac{6!}{2!}$
  2. $\displaystyle \frac{6!}{3!}\times\frac{6!}{2!}$
  3. $\displaystyle \frac{6!\times6!}{3!2!2!}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

INTERMEDIATE has 12 letters: 6 vowels (I, E, E, I, A, E) and 6 consonants (N, T, R, M, D, T). Vowels: I(2), E(3), A(1). Consonants: T(2), N(1), R(1), M(1), D(1). Permutations of vowels = 6! / (2!3!) = 60. Permutations of consonants = 6! / 2! = 360. Total = 60 * 360 = 21600. The expression 6!*6! / (3!2!2!) = 720*720 / 24 = 21600.