permutation and combination - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination/ 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 - Wikitechy https://www.wikitechy.com/interview-questions/tag/permutation-and-combination/ 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 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 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 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 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
]]> https://www.wikitechy.com/interview-questions/permutation-and-combination/how-many-ways-the-letters-of-the-word-armour-can-be-arranged/feed/ 0