Permutations & Combinations for Competitive Exam Success

Permutations & Combinations

Q. From a deck of 52 cards, how many ways can you choose 5 cards?

A. 2598960
B. 1001
C. 3125
D. 1024

Solution

The number of ways to choose 5 cards from 52 is 52C5 = 2598960.

Correct Answer: A — 2598960

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Q. From a group of 8 people, how many ways can a team of 3 be selected? (2022)

A. 56
B. 24
C. 36
D. 48

Solution

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

Correct Answer: A — 56

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Q. How many different ways can 4 students be selected from a class of 10?

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

Solution

The number of ways to choose 4 students from 10 is 10C4 = 210.

Correct Answer: A — 210

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Q. How many ways can 10 different items be selected from a group of 15? (2023)

A. 3003
B. 5005
C. 1001
D. 2002

Solution

The number of ways to choose 10 items from 15 is given by 15C10 = 15C5 = 3003.

Correct Answer: A — 3003

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Q. How many ways can 2 boys and 2 girls be selected from a group of 5 boys and 5 girls? (2023)

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

Solution

The number of ways is 5C2 * 5C2 = 10 * 10 = 100.

Correct Answer: B — 120

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Q. How many ways can 2 boys and 3 girls be selected from 6 boys and 4 girls? (2023)

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

Solution

The number of ways is 6C2 * 4C3 = 15 * 4 = 60.

Correct Answer: A — 60

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Q. How many ways can 2 boys and 3 girls be selected from a group of 6 boys and 4 girls? (2023)

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

Solution

The number of ways is 6C2 * 4C3 = 15 * 4 = 60.

Correct Answer: A — 60

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Q. How many ways can 2 boys and 3 girls be selected from a group of 6 boys and 8 girls? (2020)

A. 280
B. 300
C. 240
D. 360

Solution

The number of ways is 6C2 * 8C3 = 15 * 56 = 840.

Correct Answer: A — 280

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Q. How many ways can 2 men and 3 women be selected from a group of 5 men and 6 women? (2020)

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

Solution

The number of ways to select 2 men from 5 is 5C2 and 3 women from 6 is 6C3. Total = 5C2 * 6C3 = 10 * 20 = 200.

Correct Answer: A — 100

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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 4 men and 3 women be arranged in a line if the men must be together? (2019)

A. 5040
B. 720
C. 840
D. 1200

Solution

Treat the 4 men as one unit. Thus, we have 4 units (1 man unit + 3 women) to arrange: 4! * 4! = 24 * 24 = 576.

Correct Answer: A — 5040

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Q. How many ways can 4 students be selected from a class of 10? (2020)

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

Solution

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

Correct Answer: A — 210

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Q. How many ways can 5 different flags be arranged on a pole? (2019)

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

Solution

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

Correct Answer: B — 120

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

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

Solution

The number of arrangements around a circular table is (n-1)! = 5! = 120.

Correct Answer: A — 720

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Q. How many ways can 6 people be seated at a round table? (2020)

A. 720
B. 120
C. 600
D. 480

Solution

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

Correct Answer: A — 720

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

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

Solution

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

Correct Answer: A — 10

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Permutations & Combinations

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