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

In how many other ways can the letters of the word $'MULTIPLE'$ be arranged Without changing the order of the vowels
  1. $3359$
  2. $4400$
  3. $3524$
  4. $5200$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Word MULTIPLE has 8 letters: M, U, L, T, I, P, L, E. Vowels are U, I, E (3). Consonants are M, L, T, P, L (5). Total arrangements = 8! / 2! = 20160. If vowels must stay in order, we divide by 3! = 6. 20160 / 6 = 3360. Subtracting the original arrangement gives 3359.

Multiple choice

The number of ways in which the letters of the word "PROPORTION" is arranged without changing the relative positions of the vowels and consonants is
  1. $720$
  2. $\dfrac{4!}{2!}\cdot 6!$
  3. $\dfrac{4!}{3!}\cdot 6!$
  4. $\dfrac{4! 6!}{2! 3!}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

PROPORTION has 10 letters: P, R, O, P, O, R, T, I, O, N. Vowels are O, O, I, O (4). Consonants are P, R, P, R, T, N (6). The vowels occupy 4 fixed positions and consonants occupy 6 fixed positions. Ways to arrange vowels = 4! / 3! = 4. Ways to arrange consonants = 6! / (2! * 2!) = 180. Total ways = 4 * 180 = 720.

Multiple choice

The number of ways of arranging the letters $AAAAA, BBB, CCC< D, EE$ and $F$ in a row if the letters $C$ are separated from one another is:
  1. ${ _{ }^{ 13 }{ C } }_{ 3 }\cfrac { 12! }{ 5!3!2! } $
  2. $\cfrac{13!}{5!3!3!2!}$
  3. $\cfrac{14!}{5!3!2!}$
  4. $\cfrac{15!}{3!{(3!)}^{2}!}-\cfrac{13!}{5!3!2!}-\cfrac{12!}{5!3!}{ _{ }^{ 13 }{ C } }_{ 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Arrange the non-C letters first, giving 12!/(5!3!2!) arrangements. These letters create 13 gaps, and choosing 3 distinct gaps for the separated C letters gives C(13,3) × 12!/(5!3!2!).

Multiple choice

Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of a dictionary Number of ways (words) in which neither two A's nor two R's comes together
  1. $240$
  2. $360$
  3. $660$

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

The word ARRANGE has 7 letters: A, A, R, R, N, G, E. To ensure no two A's and no two R's are together, we use the gap method. First, arrange the 3 letters N, G, E in 3! = 6 ways. There are 4 gaps created. We place the 2 A's in 4C2 ways and 2 R's in 2C2 ways. Total = 6 * 6 * 1 * (2!/2!) * (2!/2!) is not correct; the actual calculation involves placing A's and R's into the slots. The correct count is 660.