Permutation and Combination Problems and Solutions - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination-problems-and-solutions/ Interview Questions Mon, 13 Sep 2021 09:17:40 +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 Permutation and Combination Problems and Solutions - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination-problems-and-solutions/ 32 32 There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed ? https://www.wikitechy.com/interview-questions/permutation-and-combination/there-are-25-students-in-a-class-find-the-number-of-ways-in-which-a-committee-of-3-students-is-to-be-formed/ https://www.wikitechy.com/interview-questions/permutation-and-combination/there-are-25-students-in-a-class-find-the-number-of-ways-in-which-a-committee-of-3-students-is-to-be-formed/#respond Tue, 17 Aug 2021 21:00:25 +0000 https://www.wikitechy.com/interview-questions/?p=1953

There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed ?

A . 2200

B . 2300

C . 2400

D . 3200

Answer : D . 3200

Explanation:

The number of ways = 25c3
= (25 x 24 x 23) / (1 x 2 x 3)
= 2300

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/there-are-25-students-in-a-class-find-the-number-of-ways-in-which-a-committee-of-3-students-is-to-be-formed/feed/ 0 In how many ways, the letters of the word ‘BANKING’ can be arranged ? https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-ways-the-letters-of-the-word-banking-can-be-arranged/ https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-ways-the-letters-of-the-word-banking-can-be-arranged/#respond Tue, 17 Aug 2021 20:52:23 +0000 https://www.wikitechy.com/interview-questions/?p=1949

In how many ways, the letters of the word ‘BANKING’ can be arranged ?

A. 5040

B. 2540

C. 5080

D. 2520

Answer : D. 2520

Explanation:

Total letters = 7, but N has come twice.
So, the required number of arrangements
= 7! / 2!
= 7 × 6 × 5 × 4 × 3 × 2! / 2!
= 2520

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-ways-the-letters-of-the-word-banking-can-be-arranged/feed/ 0 In how many different ways, can the letters of the word ‘INHALE’ be arranged ? https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-can-the-letters-of-the-word-inhale-be-arranged/ https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-can-the-letters-of-the-word-inhale-be-arranged/#respond Tue, 17 Aug 2021 20:50:16 +0000 https://www.wikitechy.com/interview-questions/?p=1948

In how many different ways, can the letters of the word ‘INHALE’ be arranged ?

A. 720

B. 360

C. 120

D. 650

Answer : A. 720

Explanation :

The word ‘INHALE’ has 6 particular letters .
Number of courses of action = n !
= 6 ! = 6 x 5 x 4 x 3 x 2 x 1
= 720

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-can-the-letters-of-the-word-inhale-be-arranged/feed/ 0 8 men entered a lounge simultaneously. If each person shakes hand with the other, then find the total no. of handshakes ? https://www.wikitechy.com/interview-questions/permutation-and-combination/8-men-entered-a-lounge-simultaneously-if-each-person-shakes-hand-with-the-other-then-find-the-total-no-of-handshakes/ https://www.wikitechy.com/interview-questions/permutation-and-combination/8-men-entered-a-lounge-simultaneously-if-each-person-shakes-hand-with-the-other-then-find-the-total-no-of-handshakes/#respond Tue, 17 Aug 2021 20:46:52 +0000 https://www.wikitechy.com/interview-questions/?p=1946

8 men entered a lounge simultaneously. If each person shakes hand with the other, then find the total no. of handshakes ?

A. 16

B. 36

C. 56

D. 28

Answer : C. 28

Explanation:

Required no. of hand shakes = { 8 x (8 – 1) } / 2 = 28

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/8-men-entered-a-lounge-simultaneously-if-each-person-shakes-hand-with-the-other-then-find-the-total-no-of-handshakes/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 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 In how many ways, a group of 3 boys and 2 girls can be formed out of a total of 4 boys and 4 girls ? https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-ways-a-group-of-3-boys-and-2-girls-can-be-formed-out-of-a-total-of-4-boys-and-4-girls/ https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-ways-a-group-of-3-boys-and-2-girls-can-be-formed-out-of-a-total-of-4-boys-and-4-girls/#respond Tue, 17 Aug 2021 20:01:43 +0000 https://www.wikitechy.com/interview-questions/?p=1927

In how many ways, a group of 3 boys and 2 girls can be formed out of a total of 4 boys and 4 girls ?

A. 15

B. 16

C. 20

D. 24

E. None

Answer : D. 24

Explanation:

Total number of ways = ( select 3 boys from group of 4 boys ) * ( 2 girls from group of 4 girls )
= ( 4C3 ) * ( 4C2 )
= 24

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