permutation and combination problems with solutions - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination-problems-with-solutions/ 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 permutation and combination problems with solutions - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination-problems-with-solutions/ 32 32 If 56Pr+ 6 : 54Pr + 3 = 30800 : 1 then the value of r is ? https://www.wikitechy.com/interview-questions/permutation-and-combination/if-56pr-6-54pr-3-30800-1-then-the-value-of-r-is/ https://www.wikitechy.com/interview-questions/permutation-and-combination/if-56pr-6-54pr-3-30800-1-then-the-value-of-r-is/#respond Tue, 17 Aug 2021 20:57:58 +0000 https://www.wikitechy.com/interview-questions/?p=1952

If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is ?

A. 40

B. 41

C. 42

D. None of these

Answer : B. 41

Explanation :

56Pr + 6 = 56! / [56 – (r + 6) ]! = 56! / (50 – r)!
54Pr + 3 = 54! / [54 – (r + 3) ]! = 54! / (51 – r)!
56Pr + 6 / 54Pr + 3 = [ ( 56! / (50 – r)! ) x ( (51 – r)! / 54!) ] ( 56 x 55 x 54! / (50 – r)! ) x ( (51-r).(50-r)! ) / 54 !
= 56 x 55 x (51-r)

56Pr + 6 / 54Pr + 3 = 30800 / 1
=> 56 x 55 x (51-r) = 30800
=> (51-r) = 10
=> r = 41

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/if-56pr-6-54pr-3-30800-1-then-the-value-of-r-is/feed/ 0 In a meeting between two countries, each country has 12 delegates. All the delegates of one country shake hands with all delegates of the other country. Find the number of handshakes possible ? https://www.wikitechy.com/interview-questions/permutation-and-combination/in-a-meeting-between-two-countries-each-country-has-12-delegates-all-the-delegates-of-one-country-shake-hands-with-all-delegates-of-the-other-country-find-the-number-of-handshakes-possible/ https://www.wikitechy.com/interview-questions/permutation-and-combination/in-a-meeting-between-two-countries-each-country-has-12-delegates-all-the-delegates-of-one-country-shake-hands-with-all-delegates-of-the-other-country-find-the-number-of-handshakes-possible/#respond Tue, 17 Aug 2021 20:54:03 +0000 https://www.wikitechy.com/interview-questions/?p=1950

In a meeting between two countries, each country has 12 delegates. All the delegates of one country shake hands with all delegates of the other country. Find the number of handshakes possible ?

A . 72

B . 144

C . 288

D . 234

Answer : B . 144

Explanation:

Total number of handshakes = 12 x 12 = 144

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/in-a-meeting-between-two-countries-each-country-has-12-delegates-all-the-delegates-of-one-country-shake-hands-with-all-delegates-of-the-other-country-find-the-number-of-handshakes-possible/feed/ 0 Find the value of 5P2 ? https://www.wikitechy.com/interview-questions/permutation-and-combination/find-the-value-of-5p2/ https://www.wikitechy.com/interview-questions/permutation-and-combination/find-the-value-of-5p2/#respond Tue, 17 Aug 2021 20:48:40 +0000 https://www.wikitechy.com/interview-questions/?p=1947

Find the value of 5P2 ?

A . 15

B . 18

C . 20

D . 122

Answer : C . 20

Explanation :

5P2 = 5 ! / (5 – 2) ! = 5 x 4 = 20

]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/find-the-value-of-5p2/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 A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours ? https://www.wikitechy.com/interview-questions/permutation-and-combination/a-box-contains-4-red-3-white-and-2-blue-balls-three-balls-are-drawn-at-random-find-out-the-number-of-ways-of-selecting-the-balls-of-different-colours/ https://www.wikitechy.com/interview-questions/permutation-and-combination/a-box-contains-4-red-3-white-and-2-blue-balls-three-balls-are-drawn-at-random-find-out-the-number-of-ways-of-selecting-the-balls-of-different-colours/#respond Tue, 17 Aug 2021 20:13:11 +0000 https://www.wikitechy.com/interview-questions/?p=1932

A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours ?

A. 12

B. 24

C. 48

D. 168

Answer : B. 24

Explanation:

1 red ball can be selected in 4C1 ways 1 white ball can be selected in 3C1 ways 1 blue ball can be selected in 2C1 ways
Total number of ways = 4C1 x 3C1 x 2C1 = 4 x 3 x 2 = 24.

 

  • Please note that we have multiplied the combination results, we use to add when their is OR condition, and we use to multiply when there is AND condition.
  • In this question it is AND as 1 red AND 1 White AND 1 Blue, so we multiplied
]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/a-box-contains-4-red-3-white-and-2-blue-balls-three-balls-are-drawn-at-random-find-out-the-number-of-ways-of-selecting-the-balls-of-different-colours/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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