Permutation and Combination for Competitive Exam Success

Permutation and Combination

Q. 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 is 6! / (3!) = 20.

Correct Answer: B — 30

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Q. How many ways can you choose 2 fruits from 5 different fruits?

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

Solution

The number of ways to choose 2 fruits from 5 is C(5, 2) = 5! / (2! * (5-2)!) = 10.

Correct Answer: A — 10

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Q. How many ways can you select 3 out of 7 different colored shirts?

A. 35
B. 21
C. 7
D. 14

Solution

The number of ways to select 3 shirts from 7 is C(7, 3) = 35.

Correct Answer: A — 35

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Q. How many ways can you select 4 cards from a deck of 52 cards?

A. 270725
B. 130816
C. 22100
D. 10000

Solution

The number of ways to select 4 cards from 52 is C(52, 4) = 270725.

Correct Answer: A — 270725

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Q. If a committee of 4 members is to be formed from 8 people, how many different committees can be formed?

A. 70
B. 56
C. 28
D. 12

Solution

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

Correct Answer: B — 56

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Q. In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

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

Solution

The number of ways to select 2 boys from 5 is C(5, 2) and 2 girls from 4 is C(4, 2). Total = C(5, 2) * C(4, 2) = 10 * 6 = 60.

Correct Answer: A — 60

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Q. In how many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?

A. 100
B. 120
C. 150
D. 200

Solution

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

Correct Answer: B — 120

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Q. In how many ways can 2 out of 5 different fruits be selected?

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

Solution

The number of ways to choose 2 fruits from 5 is C(5, 2) = 10.

Correct Answer: A — 10

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

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

Solution

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

Correct Answer: A — 60

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Q. In how many ways can 3 different trophies be awarded to 10 students?

A. 720
B. 1000
C. 120
D. 300

Solution

The number of ways to award 3 trophies to 10 students is 10P3 = 720.

Correct Answer: A — 720

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Q. In how many ways can 3 students be selected from a group of 10?

A. 120
B. 90
C. 100
D. 80

Solution

The number of ways to choose 3 students from 10 is C(10, 3) = 120.

Correct Answer: A — 120

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Q. In how many ways can 4 different books be chosen from a shelf of 10?

A. 210
B. 120
C. 60
D. 30

Solution

The number of ways to choose 4 books from 10 is C(10, 4) = 210.

Correct Answer: A — 210

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

A. 16
B. 24
C. 32
D. 48

Solution

The number of arrangements is 4! = 24.

Correct Answer: B — 24

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Q. In how many ways can 4 different prizes be awarded to 10 students?

A. 5040
B. 720
C. 100
D. 40

Solution

The number of ways to award 4 different prizes to 10 students is P(10, 4) = 10! / (10-4)! = 5040.

Correct Answer: A — 5040

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

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

Solution

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

Correct Answer: B — 12

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

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

Solution

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

Correct Answer: A — 120

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Q. In how many ways can 5 different books be arranged on a shelf if 2 specific books must be together?

A. 48
B. 120
C. 60
D. 24

Solution

Treat the 2 specific books as one unit. Then, we have 4 units to arrange: 4! × 2! = 48.

Correct Answer: A — 48

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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 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 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 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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Showing 31 to 60 of 60 (2 Pages)

Permutation and Combination

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