Permutation and Combination Question & Answers


From a deck of 52 cards, a 5 card hand is dealt.How may distinct five card hands are there if the queen of spades and the four of diamonds must be in the hand?

A) 52C5 B) 50C3
C) 52C4D) 50C4
Answer:   B) 50C3

Explanation:

If the queen of spades and the four of diamonds must be in hand,we have 50 cards remaining out of which we are choosing 3.

So, \inline {\color{Blue} 50C_{3}}

Subject: Permutation and Combination - Quantitative Aptitude - Arithmetic Ability

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Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.

A) 28 B) 14
C) 21 D) 7
Answer & Explanation Answer: A) 28

Explanation:

Let x, y, z be the number of balls received by the three persons, then




 x + y + z =21


 u + 5 + v + 5 + w + 5 = 21


 u + v + w = 6


 Total number of solutions = 

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In How many ways is it possible to make a selection by taking any number of 15 fruits, namely 3 oranges, 5 apples and 7 mangoes?

A) 131 B) 191
C) 68 D) 3720
Answer & Explanation Answer: B) 191

Explanation:

Out of 15 fruits, 7 are alike of one kind, 5 are alike of a second kind and 3 are alike of a third kind.


Hence, the required number of ways = [ (7+1) (5+1) (3+1) -1] =191

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In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and B , and no two are parallel. Find the number of points of intersection of the straight lines.

A) 525 B) 535
C) 545 D) 555
Answer & Explanation Answer: B) 535

Explanation:

The number of points of intersection of 37 lines is . But 13 straight lines out of the given 37 straight lines pass through the same point A. Therefore instead of getting  points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting  points, we get only one point B.


Hence the number of intersection points of the lines is  = 535


  

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A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A) 123 B) 113
C) 246 D) 945
Answer & Explanation Answer: C) 246

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.


(i) 1 lady out of 4 and 4 gentlemen out of 6


(ii) 2 ladies out of 4 and 3 gentlemen out of 6


(iii) 3 ladies out of 4 and 2 gentlemen out of 6


(iv) 4 ladies out of 4 and 1 gentlemen out of 6


In case I the number of ways =  = 4 x 15 = 60


In case II the number of ways =  = 6 x 20 = 120


In case III the number of ways =  = 4 x 15 = 60


In case IV the number of ways =  = 1 x 6 = 6


Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

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In a G - 20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharraf.

A) 2 x (17!) B) 2 x (18!)
C) (3!) x (18!) D) (17!)
Answer & Explanation Answer: B) 2 x (18!)

Explanation:

A person can be choosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf , Manmohan and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways.


 Required number of permutations = 18 x (17!) x 2 = 2 x 18!

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