Permutation and Combination for Competitive Exam Success

Permutation and Combination

Q. In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be placed?

A. 60
B. 120
C. 30
D. 90

Solution

The number of ways to select and arrange 3 books from 5 is P(5, 3) = 5! / (5-3)! = 60.

Correct Answer: B — 120

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Q. In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be displayed at a time?

A. 60
B. 120
C. 30
D. 90

Solution

The number of ways to select and arrange 3 books from 5 is 5P3 = 60.

Correct Answer: A — 60

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

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

Solution

The number of ways to distribute 5 different prizes among 3 students is 3^5 = 243.

Correct Answer: A — 243

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Q. In how many ways can 5 different shirts be arranged in a closet?

A. 120
B. 60
C. 30
D. 90

Solution

The number of arrangements of 5 different shirts is 5! = 120.

Correct Answer: A — 120

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Q. In how many ways can 5 different trophies be awarded to 3 students?

A. 60
B. 100
C. 30
D. 20

Solution

The number of ways to award 5 trophies to 3 students is 3^5 = 243.

Correct Answer: A — 60

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Q. In how many ways can 6 different books be arranged on a shelf if 2 specific books must be together?

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

Solution

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

Correct Answer: B — 720

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Q. In how many ways can 6 different books be selected and arranged on a shelf?

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

Solution

The number of ways to select and arrange 6 books is 6! = 720.

Correct Answer: A — 720

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Q. In how many ways can 6 people be seated around a circular table?

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

Solution

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

Correct Answer: B — 120

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Q. In how many ways can 6 people be seated at a round table?

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

Solution

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

Correct Answer: A — 120

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Q. In 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. In how many ways can 7 different books be arranged if 3 specific books must be on the top?

A. 720
B. 120
C. 5040
D. 840

Solution

The 3 specific books can be arranged in 3! = 6 ways. The remaining 4 books can be arranged in 4! = 24 ways. Total = 6 * 24 = 144.

Correct Answer: A — 720

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Q. In how many ways can 7 different books be arranged on a shelf if 3 specific books must be in the middle?

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

Solution

Arrange the 3 specific books in the middle (3!) and the remaining 4 books (4!): 3! * 4! = 1440.

Correct Answer: B — 1440

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Q. In how many ways can a committee of 2 be formed from 5 people?

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

Solution

The number of ways to form a committee of 2 from 5 is C(5, 2) = 10.

Correct Answer: A — 10

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Q. In how many ways can the letters of the word 'BANANA' be arranged?

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

Solution

The number of arrangements of the letters in 'BANANA' is 6! / (3!) = 20.

Correct Answer: B — 30

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Q. In how many ways can the letters of the word 'MATH' be arranged?

A. 24
B. 12
C. 6
D. 4

Solution

The number of ways to arrange the letters of 'MATH' is 4! = 24.

Correct Answer: A — 24

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Permutation and Combination

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