Permutation and Combination for Competitive Exam Success

Permutation and Combination

Q. From a group of 8 people, how many ways can a committee of 3 be formed?

A. 56
B. 24
C. 8
D. 12

Solution

The number of ways to form a committee of 3 from 8 is C(8, 3) = 56.

Correct Answer: A — 56

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Q. From a group of 8 people, how many ways can a committee of 4 be formed?

A. 70
B. 56
C. 80
D. 90

Solution

The number of ways to form a committee of 4 from 8 is C(8, 4) = 70.

Correct Answer: A — 70

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Q. How many different 4-digit PIN codes can be formed using the digits 0-9 if digits cannot be repeated?

A. 5040
B. 10000
C. 9000
D. 1000

Solution

The number of different 4-digit PIN codes is P(10, 4) = 10! / (10-4)! = 5040.

Correct Answer: A — 5040

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Q. How many different 4-digit PIN codes can be formed using the digits 0-9 if repetition is allowed?

A. 10000
B. 1000
C. 5000
D. 9000

Solution

The number of 4-digit PIN codes is 10^4 = 10000.

Correct Answer: A — 10000

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Q. How many different 4-digit PIN codes can be formed using the digits 0-9 without repetition?

A. 5040
B. 10000
C. 9000
D. 1000

Solution

The number of different 4-digit PIN codes is P(10, 4) = 10! / (10-4)! = 5040.

Correct Answer: A — 5040

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Q. How many different ways can 2 boys and 2 girls be selected from a group of 5 boys and 4 girls?

A. 60
B. 40
C. 20
D. 30

Solution

The number of ways is C(5, 2) * C(4, 2) = 10 * 6 = 60.

Correct Answer: A — 60

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Q. How many different ways can 3 letters be chosen from the word 'APPLE'?

A. 10
B. 15
C. 20
D. 5

Solution

The number of ways to choose 3 letters from 'APPLE' (considering 'P' is repeated) is C(5, 3) = 10.

Correct Answer: A — 10

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Q. How many different ways can 3 letters be chosen from the word 'COMPUTER'?

A. 56
B. 70
C. 80
D. 90

Solution

The number of ways to choose 3 letters from 8 is C(8, 3) = 56.

Correct Answer: A — 56

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Q. How many different ways can 3 students be selected from a group of 10?

A. 120
B. 720
C. 10
D. 100

Solution

The number of ways to select 3 students from 10 is C(10, 3) = 10! / (3! * (10-3)!) = 120.

Correct Answer: A — 120

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Q. How many different ways can the letters of the word 'BANANA' be arranged?

A. 60
B. 120
C. 30
D. 20

Solution

The number of arrangements is 6! / (3!) = 20.

Correct Answer: C — 30

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Q. How many different ways can the letters of the word 'LEVEL' be arranged?

A. 60
B. 30
C. 20
D. 10

Solution

The number of arrangements of 'LEVEL' is 5! / (2! * 2!) = 30.

Correct Answer: A — 60

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Q. How many ways can 10 different trophies be awarded to 3 different winners?

A. 1000
B. 720
C. 1200
D. 100

Solution

The number of ways to award trophies is P(10, 3) = 10! / (10-3)! = 720.

Correct Answer: A — 1000

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Q. How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 6 girls?

A. 100
B. 60
C. 80
D. 120

Solution

The number of ways is C(5, 2) * C(6, 3) = 10 * 20 = 200.

Correct Answer: A — 100

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Q. How many ways can 3 different prizes be awarded to 5 students?

A. 60
B. 100
C. 120
D. 30

Solution

The number of ways to award 3 prizes to 5 students is P(5, 3) = 60.

Correct Answer: C — 120

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Q. How many ways can 4 different books be arranged on a shelf if 2 specific books must be together?

A. 48
B. 24
C. 36
D. 60

Solution

Treat the 2 specific books as one unit. So, we have 3 units to arrange: (2 books together + 2 other books) = 3! * 2! = 12.

Correct Answer: A — 48

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Q. How many ways can 4 different colored balls be arranged in a row?

A. 24
B. 16
C. 12
D. 8

Solution

The number of ways to arrange 4 different colored balls is 4! = 24.

Correct Answer: A — 24

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Q. How many ways can 4 people be seated at a round table?

A. 6
B. 12
C. 24
D. 30

Solution

The number of arrangements of 4 people at a round table is (4-1)! = 3! = 6.

Correct Answer: A — 6

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Q. How many ways can 4 people be selected from a group of 12?

A. 495
B. 300
C. 400
D. 600

Solution

The number of ways to select 4 people from 12 is C(12, 4) = 495.

Correct Answer: A — 495

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Q. How many ways can 5 books be arranged on a shelf?

A. 60
B. 120
C. 100
D. 24

Solution

The number of arrangements of 5 distinct books is 5! = 120.

Correct Answer: B — 120

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Q. How many ways can 5 different books be chosen from a shelf of 15 books?

A. 3003
B. 5005
C. 1001
D. 1365

Solution

The number of ways to choose 5 books from 15 is C(15, 5) = 3003.

Correct Answer: A — 3003

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Q. How many ways can 5 different books be selected and arranged on a shelf?

A. 120
B. 60
C. 30
D. 24

Solution

The number of ways to select and arrange 5 books is 5! = 120.

Correct Answer: A — 120

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Q. How many ways can 5 different colored balls be placed in 3 different boxes?

A. 243
B. 125
C. 3125
D. 729

Solution

Each ball can go into any of the 3 boxes, so the total ways = 3^5 = 243.

Correct Answer: A — 243

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Q. How many ways can 5 different letters be arranged if 2 letters must be together?

A. 48
B. 60
C. 72
D. 80

Solution

Treat the 2 letters as one unit, so we have 4 units to arrange: 4! * 2! = 48.

Correct Answer: C — 72

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Q. How many ways can 5 different prizes be awarded to 3 students if each student can receive more than one prize?

A. 243
B. 125
C. 81
D. 64

Solution

Each prize can go to any of the 3 students, so there are 3^5 = 243 ways.

Correct Answer: A — 243

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Q. How many ways can 5 different prizes be distributed among 3 students?

A. 243
B. 125
C. 60
D. 30

Solution

Each prize can go to any of the 3 students. Therefore, the total ways = 3^5 = 243.

Correct Answer: A — 243

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Q. How many ways can 6 different colored balls be arranged in a row?

A. 720
B. 600
C. 840
D. 480

Solution

The number of arrangements of 6 different colored balls is 6! = 720.

Correct Answer: A — 720

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Q. How many ways can 6 people be seated in a round table?

A. 720
B. 120
C. 60
D. 30

Solution

The number of ways to arrange 6 people in a round table is (6-1)! = 5! = 120.

Correct Answer: A — 720

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Q. How many ways can 6 people be seated in a row if two specific people must sit next to each other?

A. 120
B. 720
C. 240
D. 60

Solution

Treat the two specific people as one unit. Then, we have 5 units to arrange: 5! = 120. The two people can be arranged in 2! ways. Total = 120 * 2 = 240.

Correct Answer: A — 120

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Q. How many ways can 7 different books be arranged on a shelf if 2 specific books must be together?

A. 720
B. 1440
C. 5040
D. 840

Solution

Treat the 2 specific books as one unit. Then, arrange 6 units: 6! * 2! = 1440.

Correct Answer: B — 1440

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Q. How many ways can a committee of 3 be formed from 8 people?

A. 56
B. 48
C. 40
D. 36

Solution

The number of ways to form a committee is C(8,3) = 56.

Correct Answer: A — 56

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Permutation and Combination

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