Permutations and Combinations Solved Examples - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutations-and-combinations-solved-examples/ Interview Questions Fri, 17 Sep 2021 11:19:07 +0000 en-US hourly 1 https://wordpress.org/?v=6.9 https://www.wikitechy.com/interview-questions/wp-content/uploads/2025/10/cropped-wikitechy-icon-32x32.png Permutations and Combinations Solved Examples - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutations-and-combinations-solved-examples/ 32 32 A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw ? https://www.wikitechy.com/interview-questions/permutation-and-combination/a-box-contains-2-white-balls-3-black-balls-and-4-red-balls-in-how-many-ways-can-3-balls-be-drawn-from-the-box-if-at-least-one-black-ball-is-to-be-included-in-the-draw/ https://www.wikitechy.com/interview-questions/permutation-and-combination/a-box-contains-2-white-balls-3-black-balls-and-4-red-balls-in-how-many-ways-can-3-balls-be-drawn-from-the-box-if-at-least-one-black-ball-is-to-be-included-in-the-draw/#respond Tue, 17 Aug 2021 20:16:50 +0000 https://www.wikitechy.com/interview-questions/?p=1934

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw ?

A. 32

B. 48

C. 64

D. 96

E. None of these

Answer : C. 64

Explanation:

We may have ( 1 black and 2 non-black ) or ( 2 black and 1 non- black ) or ( 3 black ).
Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3) = 64.

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/a-box-contains-2-white-balls-3-black-balls-and-4-red-balls-in-how-many-ways-can-3-balls-be-drawn-from-the-box-if-at-least-one-black-ball-is-to-be-included-in-the-draw/feed/ 0 In how many different ways the letters of the word ‘MATHEMATICS’ can be arranged so that the vowels always come together ? https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-the-letters-of-the-word-mathematics-can-be-arranged-so-that-the-vowels-always-come-together/ https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-the-letters-of-the-word-mathematics-can-be-arranged-so-that-the-vowels-always-come-together/#respond Tue, 17 Aug 2021 20:15:13 +0000 https://www.wikitechy.com/interview-questions/?p=1933

In how many different ways the letters of the word “MATHEMATICS” can be arranged so that the vowels always come together ?

A. 10080

B. 4989600

C. 120960

D. None of these

Answer : C. 120960

Explanation:

In the word ‘MATHEMATICS’, we treat the vowels AEAI as one letter. Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8! / (2!)(2!) = 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different. Number of ways of arranging these letters = 4! / 2! = 12.
Required number of words = (10080 x 12) = 120960.

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-the-letters-of-the-word-mathematics-can-be-arranged-so-that-the-vowels-always-come-together/feed/ 0 How many words can be formed from the letters of the word “AFTER”, so that the vowels never come together ? https://www.wikitechy.com/interview-questions/permutation-and-combination/how-many-words-can-be-formed-from-the-letters-of-the-word-after-so-that-the-vowels-never-come-together/ https://www.wikitechy.com/interview-questions/permutation-and-combination/how-many-words-can-be-formed-from-the-letters-of-the-word-after-so-that-the-vowels-never-come-together/#respond Tue, 17 Aug 2021 20:10:43 +0000 https://www.wikitechy.com/interview-questions/?p=1931

How many words can be formed from the letters of the word AFTER, so that the vowels never come together ?

A. 48

B. 52

C. 72

D. 120

Answer : C. 72

Explanation:

We need to find the ways that vowels NEVER come together.
Vowels are A, E Let the word be FTR(AE) having 4 words.
Total ways = 4! = 24
Vowels can have total ways 2! = 2
Number of ways having vowel together = 48
Total number of words using all letter = 5! = 120.
Number of words having vowels never together = 120 – 48 = 72

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/how-many-words-can-be-formed-from-the-letters-of-the-word-after-so-that-the-vowels-never-come-together/feed/ 0 Evaluate permutation equation 59P3 ? https://www.wikitechy.com/interview-questions/permutation-and-combination/evaluate-permutation-equation-59p3/ https://www.wikitechy.com/interview-questions/permutation-and-combination/evaluate-permutation-equation-59p3/#respond Tue, 17 Aug 2021 20:08:47 +0000 https://www.wikitechy.com/interview-questions/?p=1930

Evaluate permutation equation 59P3 ?

A. 195052

B. 195053

C. 195054

D. 185054

Answer : C. 195054

Explanation:

nPr = n! / (n−r)!
59P3 = 59! / (56)!
= 59 ∗ 58 ∗ 57 ∗ 56! / (56)!
=195054

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/evaluate-permutation-equation-59p3/feed/ 0 Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ? https://www.wikitechy.com/interview-questions/permutation-and-combination/out-of-7-consonants-and-4-vowels-how-many-words-of-3-consonants-and-2-vowels-can-be-formed/ https://www.wikitechy.com/interview-questions/permutation-and-combination/out-of-7-consonants-and-4-vowels-how-many-words-of-3-consonants-and-2-vowels-can-be-formed/#respond Tue, 17 Aug 2021 20:04:36 +0000 https://www.wikitechy.com/interview-questions/?p=1928

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?

A. 210

B. 1050

C. 25200

D. 21400

E. None of these

Answer : C. 25200

Explanation:

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2)
= { (7 x 6 x 5) / (3 x 2 x 1) } x { (4 x 3) / (2 x 1) } = 210.
Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120.

Required number of ways = (210 x 120) = 25200.

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/out-of-7-consonants-and-4-vowels-how-many-words-of-3-consonants-and-2-vowels-can-be-formed/feed/ 0 How many ways the letters of the word ‘ARMOUR’ can be arranged ? https://www.wikitechy.com/interview-questions/permutation-and-combination/how-many-ways-the-letters-of-the-word-armour-can-be-arranged/ https://www.wikitechy.com/interview-questions/permutation-and-combination/how-many-ways-the-letters-of-the-word-armour-can-be-arranged/#respond Tue, 17 Aug 2021 19:59:42 +0000 https://www.wikitechy.com/interview-questions/?p=1926

How many ways the letters of the word “ARMOUR” can be arranged ?

A. 720

B. 300

C. 640

D. 360

E. None of these

Answer : D. 360

Explanation:

  • Total number of letters = 6 and R is repeated twice.
  • Required arrangements = (6! / 2!) = 360
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