Permutation and Combination- Aptitude Questions and Answers

View in English View in Hindi

If 10 persons meet at a meeting and shake hands exactly once with each other, what is the total number of handshakes?

A)
35

B)
35

C)
50

D)
45


Correct Answer :

45


Explanation :

Combinations of n objects taken r at a time = nCr= n! / [r!(n-r!)]
Required number of ways = 10C2 = 10*9 / 2 = 45

Post comment
Cancel
Thanks for your comment.!
Write a comment(Click here) ...
Mahak joshi
2018-08-04 22:24:53

10 people meet and shakes hand with each other. First person will shakes hand with other 9, second person had already shakes hand with 1st person and shakes hand with other 8, third………..

So, the total no. of hand shakes= 9+8+7+6+5+4+3+2+1=45 shakes

View in English View in Hindi

By using digits 1 to 9 how many 4 digit numbers can be formed which has 5 as a unit digit? Repetition of digits is are not allowed.

A)
336

B)
1400

C)
504

D)
251


Correct Answer :

336


Explanation :

5 at the unit place or divisible by 5. So, there is 1 way of doing it.
No repetition of digits.thus there are 8 ways of filling the tens place from the remaining 8 digits (1,2,3,4,6,7,8,9).
the hundreds place can be filled by any of the remaining 7 digits. So, there are 7 ways of filling it.
the thousands place can be filled by any of the remaining 6 digits. So, there are 6 ways of filling it.

Required number of numbers = (1 * 8 * 7 * 6) = 336.

In how many ways can 5 prizes be given away to 7 boys when each boy is eligible for all the prizes?

A)
5!

B)
7!

C)
57

D)
75


Correct Answer :

75


Explanation :

A prize can be given to any one of the 7 boys in (7/1)=7 ways
So, each prize can be distributed in (7/1)=7 ways
5 prizes can be distributed in (7/1)*(7/1)*(7/1)*(7/1)*(7/1) = 75 ways

How many different words, can be formed by rearranging the letters of the word ‘SUCCESS’?

A)
5040

B)
840

C)
420

D)
1680


Correct Answer :

420


Explanation :

The word "SUCCESS" has total 7 elements, there two repeated elements S(thrice) and C(twice). The formula for permutations with repeated elements is as follows, When k out of n elements are indistinguishable, e.g. k copies of the same book, the number of different permutations is n!/k!.

Therefore the total number of arrangement of the word SUCCESS can be formed is 7!/3! *2!
=> (7*6*5*4*3*2*1)/(3*2*1)*(2*1) => 7*6*5*2 => 420

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

A)
2630

B)
5040

C)
1680

D)
3456


Correct Answer :

5040


Explanation :

There are 7 unique letters in ARCHIVE which means that there are 7!=7*6*5*4*3*2*1=5040 different ways to rearrange them.

In how many different ways can the letters of the word ‘PUBLIC’ be arranged so that the vowels are at the two ends?

A)
48

B)
72

C)
36

D)
None of these


Correct Answer :

48


Explanation :

PUBLIC has 2 vowels(UI) and 4 consonants (PBLC). All the letters are distinct.
First letter can be any of the two vowels (2 ways) and Last letter is the remaining vowel (1 way)
4 consonants can be arranged in 4! ways

Total number of ways = 2!*1!*4! = (2*1)*1*(4*3*2*1)=48

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

A)

40


B)

41


C)

42


D)

43



Correct Answer :

41


Explanation :

56Pr + 6 : 54Pr + 3 = 30800 : 1
⇒ 56! / (56 -(r + 6))! : 54! / (54 - (r + 3))! = 30800 : 1
⇒ 56! / (50 - r)! : 54! / (51 - r)! = 30800 : 1

As 56! = 56*55*54!
and also (51 - r)! =(51 - r)*[(51 - r) -1]! ⇒ (51 - r)*(50 - r)!

So,
⇒ 56*55*54! / (50 - r)! = (30800 x 54!) / (51 - r)*(50 - r)!
⇒ 56*55 = 30800/(51 - r)
⇒ 51 - r = 10
Hence, r = 41

How many groups of 6 persons can be formed from 8 men and 7 women ?

A)

5000


B)

5005


C)

5050


D)

5650



Correct Answer :

5005


Explanation :

Total number of person = 8 men + 7 women = 15
No. of groups can be formed of 6 persons= 15C6 = 15! / {6! *(15 - 6)!} = 15! / (6! * 9!)
= (15 x 14 x 13 x 12 x 11 x 10) / (6 x 5 x 4 x 3 x 2 x 1)
= 5005

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is?

A)
200

B)
216

C)
235

D)
256


Correct Answer :

200


Explanation :

Let there were g girls and b boys.
As given, total number of games in which both players were women gC2 = 45
=> g(g−1)/2=45
=> g2-g-90 = 0
(g - 10)(g + 9) = 0
So, g =10 as g ≠ -9

As given, total number of games in which both players were men bC2 = 190
=>b(b−1)/2=190
=> b2-b-380 = 0
(b - 20)(b + 190) = 0
So, b=20 as b ≠ -190

Total number of games= (g + b)C2 => 30C2 => (30 *29) / (2* 1) => 435

Number of games in which one player is a boy and the other is a girl = 435 - 45 - 190 = 200

In how many different ways can the letters of the word ‘DESIGN’ be arranged so that the vowels are at the two ends?

A)

56


B)

64


C)

24


D)

48



Correct Answer :

48


Explanation :

DESIGN has 2 vowels(EI) and 4 consonants (DSGN).
Four consonants can be arranged in 4! ways two vowels can be arranged in 2! ways

Total number of arrangements= 4!×2! = 48

Latest Updates

Indian Geography

What is the approximate distance between earth and the moon?

Indian History

In which year was the battle of ‘Koregaon Bhima’ fought?

The approach that is very useful in organizing the content in history is.

General Knowledge of India

NITI Aayog stands for _____.

General Knowledge of MP

India’s first Ramayan art museum was established at?

Errors Identification

Read the sentence carefully and choose the option that has an error in it:
The management’s trusted employee was suspected of stealing large sum of money.

Read the sentence carefully and choose the option that has an error in it:
The teacher asked the child to repeat again because he spoke feebly.

Fill in the blank

Fill in the blank with the most appropriate preposition in the given sentence.
Let’s sit _________ the shade of this beautiful tree.

Choose the most appropriate determiner for the given sentence.
________of what he said was very sensible.

Substitution

Choose the option that substitutes the given phrase appropriately.
A work of art made by carving

Correct sentence

Choose the option that best transforms the sentence into its Indirect form:
‘What country do you come from?’ said the police officer.

Alternative Phrase

Choose the option that best explains the highlighted expression:
All human beings have feet of clay.

Fill in the blank

Choose an appropriate modal for the given sentence:
My doctor said that I_____ stop smoking as one of my lungs got infected.

Choose the appropriate prepositions for the given sentence:
My parents have been married ________ forty-nine years, but you can still see the love ________ their eyes.

Choose the appropriate conjunction for the given sentence:
______ it rains, the college will declare the holiday.

Antonyms

Choose the appropriate antonym for the highlighted word in the given sentence.
The family protracted their visit by several days.

Tenses

Choose the appropriate tenses to fill in the blanks in the given sentence:
Please _________ a noise. Ritu __________ to sleep.

Synonyms

Choose the appropriate synonym for the highlighted word in the given sentence.
Does he really expect us to believe such a flimsy excuse?

Latest Job Notifications

Jobs in Bihar

बिहार तकनीकी सेवा आयोग / Bihar Technical Service Commission (BTSC) - 12771 पद - 01/09/2022 अंतिम तिथि

Jobs in Rajasthan

राजस्थान उच्च न्यायालय / Rajasthan High Court - 2756 पद - 22/09/2022 अंतिम तिथि

Jobs in Uttar Pradesh

उत्तर प्रदेश पावर कॉर्पोरेशन लिमिटेड / Uttar Pradesh Power Corporation Limited - 1033 पद - 12/09/2022 अंतिम तिथि

Jobs in Tamil Nadu

तमिलनाडु चिकित्सा सेवा भर्ती बोर्ड / Tamil Nadu Medical Services Recruitment Board (MRB) - 889 पद - 30/08/2022 अंतिम तिथि

Jobs in Andhra Pradesh

आंध्र प्रदेश स्वास्थ्य, चिकित्सा और परिवार कल्याण विभाग / Andhra Pradesh Health, Medical and Family Welfare Department - 1681 पद - 22/08/2022 अंतिम तिथि

SSC Recruitment

कर्मचारी चयन आयोग (एसएससी) Staff Selection Commission (SSC) - 4300 पद - 30/08/2022 अंतिम तिथि - CPO Recruitment

Banking Jobs

बैंकिंग कार्मिक चयन संस्थान Institute of Banking Personnel Selection(IBPS) - 6432 पद - 22/08/2022 अंतिम तिथि

बैंकिंग कार्मिक चयन संस्थान Institute of Banking Personnel Selection(IBPS) - 7855 पद - 29/07/2022 अंतिम तिथि

SSC Recruitment

कर्मचारी चयन आयोग (एसएससी) Staff Selection Commission (SSC) - 1411 पद - 29/07/2022 अंतिम तिथि

Jobs in Rajasthan

राजस्थान अधीनस्थ और मंत्रिस्तरीय सेवा चयन बोर्ड Rajasthan Subordinate and Ministerial Services Selection Board (RSMSSB) - 5546 पद - 22-Jul-2022 अंतिम तिथि