permutation and combination examples - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination-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 permutation and combination examples - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination-examples/ 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 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 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 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

]]> 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/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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