Permutations & Combinations for Competitive Exam Success

Permutations & combinations

Q. How many ways can 5 different letters be selected from the alphabet?

A. 26
B. 3003
C. 156
D. 120

Solution

The number of ways to choose 5 letters from 26 is C(26, 5) = 65780.

Correct Answer: B — 3003

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

A. 60
B. 100
C. 150
D. 200

Solution

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

Correct Answer: C — 150

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Q. 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. 480

Solution

Treat the 2 specific books as one unit. Then we have 5 units to arrange: 5! * 2! = 240.

Correct Answer: C — 240

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Q. How many ways can 6 people be arranged in a circle?

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

Solution

The number of arrangements in a circle is (n-1)! = (6-1)! = 5! = 120.

Correct Answer: A — 720

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Q. How many ways can 6 people be divided into 2 groups of 3?

A. 20
B. 30
C. 10
D. 15

Solution

The number of ways to divide 6 people into 2 groups of 3 is (6! / (3!3!)) / 2 = 20.

Correct Answer: A — 20

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Q. How many ways can a committee of 3 be formed from 5 people?

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

Solution

The number of ways to choose 3 from 5 is C(5,3) = 10.

Correct Answer: A — 10

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Q. How many ways can you arrange the letters of the word 'BANANA'?

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

Solution

The word 'BANANA' has 6 letters with 'A' repeating 3 times and 'N' repeating 2 times. The arrangements are 6!/(3!2!) = 60.

Correct Answer: B — 30

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Q. How many ways can you choose 3 fruits from a basket of 5 different fruits?

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

Solution

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

Correct Answer: A — 10

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Q. How many ways can you form a committee of 3 from a group of 10 people?

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

Solution

The number of ways to form a committee of 3 from 10 is given by 10C3 = 120.

Correct Answer: A — 120

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

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

Solution

The number of ways to choose 2 from 5 is given by 5C2 = 10.

Correct Answer: A — 10

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Q. How many ways can you select 2 students from a group of 8?

A. 28
B. 56
C. 36
D. 8

Solution

The number of ways to select 2 students from 8 is given by 8C2 = 28.

Correct Answer: A — 28

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Q. In how many ways can 3 boys and 2 girls be seated in a row?

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

Solution

The total number of arrangements is (3+2)! = 5! = 120.

Correct Answer: B — 60

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Q. In how many ways can 3 different colored balls be arranged in a line?

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

Solution

The number of arrangements of 3 different colored balls is 3! = 6.

Correct Answer: A — 6

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Q. In how many ways can 3 different colored balls be chosen from a set of 7?

A. 35
B. 21
C. 42
D. 56

Solution

The number of ways to choose 3 from 7 is given by C(7,3) = 7!/(3!4!) = 35.

Correct Answer: A — 35

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Q. In 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). The arrangements = 3! * 3! = 36.

Correct Answer: B — 120

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

A. 10
B. 15
C. 20
D. 25

Solution

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

Correct Answer: A — 10

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

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

Solution

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

Correct Answer: B — 120

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Q. In 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. In how many ways can 4 different books be selected 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. In 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. In 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. In 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 is P(4, 3) = 4! / 1! = 24.

Correct Answer: C — 36

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Q. In how many ways can 4 different prizes be distributed among 3 students?

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

Solution

Each prize can go to any of the 3 students, so the total ways = 3^4 = 81.

Correct Answer: A — 81

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Q. In how many ways can 4 students be selected from a group of 10?

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

Solution

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

Correct Answer: A — 210

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Q. In how many ways can 5 different colored balls be arranged in a box?

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

Solution

The number of arrangements is 5! = 120.

Correct Answer: B — 120

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Q. In how many ways can 5 different flags be arranged on a pole?

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

Solution

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

Correct Answer: A — 120

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Q. In how many ways can 5 different items be selected from 10 items?

A. 252
B. 120
C. 200
D. 300

Solution

The number of ways to select 5 items from 10 is C(10, 5) = 252.

Correct Answer: A — 252

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Q. In how many ways can 5 different objects be selected from 10 objects?

A. 252
B. 120
C. 10
D. 100

Solution

The number of ways to select 5 objects from 10 is 10C5 = 10! / (5! * 5!) = 252.

Correct Answer: A — 252

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Q. In how many ways can 6 different objects be selected and arranged in a line?

A. 720
B. 600
C. 840
D. 960

Solution

The number of arrangements of 6 different objects is 6! = 720.

Correct Answer: A — 720

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Q. In how many ways can 6 people be divided into 2 groups of 3?

A. 20
B. 30
C. 10
D. 15

Solution

The number of ways to divide 6 people into 2 groups of 3 is 6! / (3! * 3! * 2!) = 20.

Correct Answer: A — 20

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Showing 31 to 60 of 63 (3 Pages)

Permutations & combinations

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