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

Each question contains a statement followed by Quantity I and Quantity II. Read the contents clearly and answer your questions accordingly. Quantity I: How many numbers greater than 3 million can be formed by using the digits 4, 2, 3, 0, 3, 4, 5? Quantity II: How many words can be formed using the letters of the word “CORRESPONDING” if the consonants are always written together?

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Count 7-digit numbers > 3,000,000 from digits {4,2,3,0,3,4,5}. If first digit is 4 or 5: 2 × 720/2 = 720. If first digit is 3: remaining digits {2,0,3,4,4,5} arranged in 720/2 = 360 ways. Total = 1080. Quantity II: In CORRESPONDING, consonants CRRSPNDNG (9 letters, R repeated) must stay together. Treat consonant block + 4 vowels = 5 units. Vowels OEOI (4 distinct) arrange in 4! = 24. Within block, CRRSPNDNG has 9!/2! = 181440 arrangements. Total = 24 × 181440 = 4354560. Since 4354560 > 1080, Quantity II > Quantity I is correct.

Multiple choice

In how many different ways can the letters of the word 'ENTRANCE' be arranged in such a way that the vowels always come together ? शब्द 'ENTRANCE' के अक्षर कितने विभिन्न प्रकार से क्रमबद्ध किये जा सकते हैं ताकि स्वर एक साथ आ सके?

  1. 5120

  2. 2060

  3. 720

  4. 1080

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

ENTRANCE has 8 letters with vowels E, A, E (E repeats twice). Treat vowels as one block with consonants N, T, R, N, C. Total 6 units can be arranged in 6! ways. Vowels within their block: 3!/2! = 3 ways. Consonants: 5!/2! = 60 ways. Total = 6 × 60 × 3 = 1080.

Multiple choice

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? शब्द ' MATHEMATICS’ के अक्षरों को कितने अलग-अलग तरीकों से व्यवस्थित किया जा सकता है ताकि स्वर हमेशा एक साथ आए?

  1. 120180

  2. 120216

  3. 120320

  4. 120240

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Treating vowels (A, E, A, I) as one unit gives 8 units total. These 8 units can be arranged in 8! = 40320 ways. Within the vowel unit, the 4 vowels with A repeated twice can be arranged in 4!/2! = 12 ways. Total arrangements = 40320 × 12 = 483,840. Since none of the given options (120180, 120216, 120320, 120240) match this result, option E is correct.

Multiple choice

In how many different ways the letters of the word OUTSIDE be arranged in such a way that all vowels always come together? OUTSIDE शब्द के अक्षरों को कितने अलग-अलग तरीकों से इस तरह से व्यवस्थित किया गया है कि सभी स्वर हमेशा एक साथ आते हैं?

  1. 524

  2. 576

  3. 625

  4. 2880

  5. None of these इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The word OUTSIDE has 6 letters with vowels O, U, I, E (4 vowels) and consonants T, S, D (3 consonants). Treat the 4 vowels as one unit. So we have 4 units total (vowel block + 3 consonants) that can be arranged in 4! = 24 ways. Within the vowel block, the 4 vowels can be arranged in 4! = 24 ways. Total arrangements = 24 × 24 = 576.

Multiple choice

Select the correct option that indicates the arrangement of the given words in the order in which they appear in an English dictionary. 1. Protest 2. Palindrome 3. Probability 4. Pathetic 5. Parking

  1. 2, 5, 4, 3, 1

  2. 2, 4, 5, 3, 1

  3. 2, 5, 1, 4, 3

  4. 2, 1, 3, 4, 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Arrange the words alphabetically: Palindrome (P-a), Parking (P-a), Pathetic (P-a), Probability (P-r), Protest (P-r). Comparing Parking vs Pathetic: P-a-r-k vs P-a-t-h. 'r' comes before 't', so Parking comes before Pathetic. The order is: 2. Palindrome, 5. Parking, 4. Pathetic, 3. Probability, 1. Protest. This gives the sequence: 2, 5, 4, 3, 1.

Multiple choice

In how many different ways can the letters of the word 'CONSTRUCT' be arranged? शब्द 'CONSTRUCT' के अक्षरों को कितने प्रकार से व्यवस्थित किया जा सकता है?

  1. 362880

  2. 120960

  3. 90720

  4. 60480

  5. None of these इनमें से कोई नही
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word CONSTRUCT has 9 letters with C and T each repeating twice. Number of arrangements = 9! / (2! × 2!) = 362880 / 4 = 90720. We divide by 2! for each repeated letter to account for indistinguishable arrangements. Option C matches this result.

Multiple choice

In how many different ways can the letters of the words 'INHALE' be arranged? शब्द 'INHALE' के अक्षरों को कितने विभिन्न प्रकार से व्यवस्थित किया जा सकता है ?

  1. 720

  2. 360

  3. 120

  4. 650

  5. 2520
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The word INHALE has 6 distinct letters. The number of arrangements is 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720. All letters are different, so no repetition adjustment needed.

Multiple choice

The letters of the word ORIENTAL are arranged in all possible ways. The chance that the consonants and vowels occur alternatively is
  1. $\dfrac{1}{70}$
  2. $\dfrac{2}{35}$
  3. $\dfrac{1}{35}$
  4. $\dfrac{4}{35}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

ORIENTAL: 8 letters, 4 vowels (O, I, E, A), 4 consonants (R, N, T, L). Total arrangements = 8!. Favorable: V C V C V C V C or C V C V C V C V. 2 * (4! * 4!) = 2 * 24 * 24 = 1152. Total = 40320. Probability = 1152/40320 = 1/35.

Multiple choice

The probability that in a random arrangement of the letters of the word $UNIVERSITY$ the $2$ Is come together is
  1. $\displaystyle \frac{3}{5}$
  2. $\displaystyle \frac{2}{5}$
  3. $\displaystyle \frac{1}{5}$
  4. $\displaystyle \frac{4}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The word UNIVERSITY has 10 letters with two I's. Treating the two I's as a single unit, we arrange 9 units in 9!/2! ways (since there are two I's, but we treat them as one block, wait: the letters are U, N, I, V, E, R, S, I, T, Y. There are 10 letters, two I's. Total arrangements = 10!/2!. Arrangements with I's together = 9! ways. Probability = 9! / (10!/2!) = 2/10 = 1/5.