Major Competitive Exams

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Q. How many ways can 3 different books be chosen from a set of 7 books?

A. 35
B. 21
C. 42
D. 28

Solution

The number of ways to choose 3 books from 7 is 7C3 = 7! / (3! * 4!) = 35.

Correct Answer: A — 35

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Q. How many ways can 3 different books be chosen from a set of 7?

A. 35
B. 42
C. 49
D. 56

Solution

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

Correct Answer: A — 35

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Q. How many ways can 3 different colored balls be arranged in a row? (2022)

A. 6
B. 3
C. 9
D. 12

Solution

The number of arrangements of 3 distinct balls is 3! = 6.

Correct Answer: A — 6

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Q. How many ways can 3 different fruits be chosen from 8 fruits?

A. 56
B. 84
C. 28
D. 36

Solution

The number of ways is C(8,3) = 56.

Correct Answer: B — 84

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Q. How many ways can 3 different fruits be selected from 5 available fruits?

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

Solution

The number of ways to choose 3 from 5 is given by 5C3 = 10.

Correct Answer: B — 15

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Q. How many ways can 3 different gifts be given to 5 children if each child can receive more than one gift? (2022)

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

Solution

Each gift can go to any of the 5 children, so the total ways = 5^3 = 125.

Correct Answer: B — 243

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

A. 120
B. 220
C. 60
D. 80

Solution

The number of ways is C(11, 3) = 165.

Correct Answer: C — 60

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Q. How many ways can 3 different trophies be awarded to 5 students? (2022)

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

Solution

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

Correct Answer: C — 120

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

A. 120
B. 60
C. 30
D. 10

Solution

The number of ways to choose 3 letters from 11 distinct letters is 11C3 = 165.

Correct Answer: B — 60

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Q. How many ways can 3 men and 2 women be arranged in a line if the men must be together?

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

Solution

Treat the 3 men as one unit. So, we have 3 units (MMM, W, W). Arrangements = 4! * 3! = 24 * 6 = 144.

Correct Answer: B — 120

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Q. How many ways can 3 out of 8 different colored balls be chosen? (2022)

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

Solution

The number of ways to choose 3 balls from 8 is given by 8C3 = 56.

Correct Answer: A — 56

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Q. How many ways can 3 prizes be awarded to 10 students if no student can win more than one prize?

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

Solution

The number of ways to award 3 prizes is P(10, 3) = 720.

Correct Answer: A — 720

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Q. How many ways can 3 red balls and 2 blue balls be arranged in a line? (2016)

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

Solution

The number of arrangements is 5! / (3! * 2!) = 10.

Correct Answer: D — 20

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Q. How many ways can 3 red balls and 2 blue balls be arranged in a row?

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

Solution

The arrangements = 5! / (3! * 2!) = 10.

Correct Answer: A — 10

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Q. How many ways can 3 red, 2 blue, and 1 green ball be arranged in a line?

A. 120
B. 60
C. 30
D. 10

Solution

The total arrangements are 6! / (3! * 2! * 1!) = 60.

Correct Answer: B — 60

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Q. How many ways can 3 red, 2 blue, and 1 green balls be arranged in a line?

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

Solution

The arrangements = 6! / (3! * 2! * 1!) = 60.

Correct Answer: A — 60

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Q. How many ways can 3 red, 2 blue, and 1 green balls be arranged in a row?

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

Solution

The total arrangements = 6! / (3! * 2! * 1!) = 60.

Correct Answer: A — 60

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Q. 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 select 3 students from 10 is given by 10C3 = 120.

Correct Answer: A — 120

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

A. 210
B. 120
C. 240
D. 300

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

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. How many ways can 4 different colored balls be placed in 3 different boxes?

A. 81
B. 64
C. 27
D. 12

Solution

Each ball can go into any of the 3 boxes, so the total ways = 3^4 = 81.

Correct Answer: A — 81

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Q. How many ways can 4 different flags be arranged on a pole? (2021)

A. 24
B. 12
C. 16
D. 20

Solution

The number of arrangements of 4 distinct flags is 4! = 24.

Correct Answer: A — 24

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Q. How many ways can 4 different fruits be selected from 6 available fruits? (2021)

A. 15
B. 30
C. 20
D. 25

Solution

The number of ways to choose 4 fruits from 6 is C(6, 4) = 15.

Correct Answer: C — 20

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Q. How many ways can 4 different fruits be selected from 8 available fruits? (2021)

A. 70
B. 80
C. 90
D. 100

Solution

The number of ways to choose 4 fruits from 8 is given by 8C4 = 70.

Correct Answer: A — 70

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Q. How many ways can 4 different fruits be selected from 8?

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

Solution

The number of ways to select 4 fruits from 8 is given by 8C4 = 70.

Correct Answer: B — 56

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Q. How many ways can 4 different fruits be selected from a basket of 10 fruits?

A. 210
B. 120
C. 300
D. 150

Solution

The number of ways to choose 4 fruits from 10 is given by 10C4 = 210.

Correct Answer: A — 210

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Q. How many ways can 4 different letters be chosen from the word 'COMBINATION'?

A. 210
B. 126
C. 70
D. 84

Solution

The number of ways to choose 4 letters from 11 distinct letters is 11C4 = 330.

Correct Answer: A — 210

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Q. How many ways can 4 different letters be chosen from the word 'COMPUTE'? (2022)

A. 35
B. 70
C. 56
D. 84

Solution

The number of ways is 8C4 = 70.

Correct Answer: C — 56

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Q. How many ways can 4 different letters be selected from the word 'COMBINATION'?

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

Solution

The number of ways to choose 4 letters from 11 distinct letters is 11C4 = 330.

Correct Answer: A — 210

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Q. How many ways can 4 different prizes be awarded to 3 students?

A. 12
B. 24
C. 36
D. 48

Solution

The number of ways to award 4 different prizes to 3 students is 3^4 = 81.

Correct Answer: C — 36

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Major Competitive Exams

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