Permutation Combination Questions and Answers

Practice Questions on Permutation and Combination

Permutation is explained as the series of r terms that can be completed out of total n number of things. Permutations are often represented by nPr which is equivalent to \frac{n!}{(n – r)!}
The various arrangement of a particular number of undertakings by assuming either few or whole at once is known as permutations. All permutations are prepared with the terms p, q, and r by compelling two at a time, they are formed as PQ, QP, pr, RP, QR, and RQ. The permutations compelled with the terms p, q and r taking all at once are:
pqr, prq, qpr, qrp, rpq, rqp.

Combination is explained as selecting r series that can be finished out of total n events. It is signified by nCr that sequentially is equivalent to \frac{n!}{r!(n-r)!}
On the basis of the basic Principle of Counting, when we are able to do a precise series in m ways as well as any additional event in assuming n ways, thus it can be supposed that:

Any one of the taken two activities can be accomplished in m + n means plus,
Two of them are able to be done in m * n ways.

Below are the Practice Questions on Permutation and Combination

Practice Questions for Permutation and Combination

Rules

  • There are certain rules that are specified for permutation and combinations. These rules contains formulas and basic know-hows which needs to be considered while solving questions related to the same. It will help you to understand the concept in a better way and to avoid mistakes in the future. To through the below given rules and formulas for gaining further understanding on the subject:
  • The number of all combinations of n things, taken r at a time is:
    ^{n}C_{r} = n! = n (n – 1) (n – 2) … to r factors.
    \frac{(n!)}{(n – r)! r!}
  • While solving question on combinations, you should know the below mentioned formulas:
    o ^{n}C_{n} = 1 \text{ and } ^{n}C_{0} = 1
    o ^{n}C_{r} = ^{n}C_{(n – r)}
  • The permutation of n events, taken r at a time, is represented as:
    ^{n}P_{r} = n(n – 1)(n – 2) … (n – r + 1) = \frac{n!}{(n – r)!}
  • Key point to know is that the statement questions are chiefly made to check your knowledge to make an equation and then put formulae for it.
  • Permutations are used when an issue calls for the number of activities of things as well as various tips are to be calculated.
  • Combinations are used when an issue arise for the number of tricks of choosing things along with the order of choice is not to be calculated.

Question 1

Time: 00:00:00
Among 9 consonants and 5 vowels, what number of words can be formed of 4 consonants and 3 vowels?

2101456

2101456

2540160

2540160

2520035

2520035

20321280

20321280

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Question 2

Time: 00:00:00
Surendra has 15 denims and 18 shirts. If he wants to choose different-2 ways for selecting denims and shirts, calculate the numbers of that?

33

33

119

119

108

108

240

240

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Question 3

Time: 00:00:00
Find out the number of arrangements that can be made for the word RAINBOW if all the the vowels are placed on the even places?

720

720

144

144

120

120

36

36

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Question 4

Time: 00:00:00
In how many ways the word 'MESMERISE' can be written?

5!/(2!)2 3!

5!/(2!)2 3!

9!/(2!)3 3!

9!/(2!)3 3!

9!/(2!)2 (2!)3

9!/(2!)2 (2!)3

9!/(2!)2 3!

9!/(2!)2 3!

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Question 5

Time: 00:00:00
A panel has total of 11 members 5 males and 6 females. Find out the number of ways of picking 2 males and 3 females from the given panel team?

110

110

300

300

200

200

350

350

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Question 6

Time: 00:00:00
There are 21 stations between Chennai and Darjeeling. Find out that what is the number of second class tickets have to be produced, so that a traveler can travel from any point of station to the any of the station?

506

506

380

380

950

950

180

180

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Question 7

Time: 00:00:00
A device password comprises 5 rings each having 7 different messages. Find out the maximum number of different unsuccessful efforts to open the lock?

22316

22316

24321

24321

16806

16806

17283

17283

17128

17128

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Question 8

Time: 00:00:00
Find out the number of ways in which 6 male teachers and 6 female teachers can be settled on seat for a shoot so that no two female teachers sit simultaneously?

2 (6!)

2 (6!)

6! * ⁷P₆

6! * ⁷P₆

1(6!) 2

1(6!) 2

9! * 6

9! * 6

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Question 9

Time: 00:00:00
By using the digits (1, 3, 4, 5, 6, 7, 8) how many five digit numbers can be made? Rule*(Recurrence of numbers is not allowed)?

3610

3610

6020

6020

2520

2520

2180

2180

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Question 10

Time: 00:00:00
Out of numbers (1, 2,3,5,7 & 9) how many four digit even numbers can be formed?

100

100

360

360

60

60

40

40

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Question 11

Time: 00:00:00
A drum comprises 9 fruits, 3 vegetables and 4 candies. In how many ways can two items be drawn from the drum?

280

280

240

240

120

120

220

220

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Question 12

Time: 00:00:00
What will be the number of ways in which three consonants and two vowels be chosen from the word "FEBRUARY"?

19

19

28

28

30

30

20

20

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Question 13

Time: 00:00:00
John is appearing for GMAT exam. In his test he got 7 questions. Each query having 3 internal options. Find out the number of ways in which john can attempt one or more questions?

6332

6332

16383