### Permutations and Combinations mcq

How many ways can the letters of the word “APPLE” be arranged?

a) 5

b) 10

c) 15

d) 20

Answer: c) 15

In how many ways can a committee of 3 people be chosen from a group of 8?

a) 8

b) 24

c) 56

d) 84

Answer: d) 84

How many 3-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?

a) 6

b) 12

c) 24

d) 36

Answer: c) 24

In how many ways can 3 prizes be distributed among 5 participants if each person can receive multiple prizes?

a) 15

b) 25

c) 50

d) 125

Answer: d) 125

A password consists of 4 letters, followed by 3 digits. How many different passwords can be created if repetition of characters and digits is allowed?

a) 7,776

b) 12,960

c) 13,824

d) 15,625

Answer: b) 12,960

How many ways can 4 books be arranged on a shelf?

a) 12

b) 16

c) 20

d) 24

Answer: d) 24

In how many ways can the letters of the word “MISSISSIPPI” be arranged?

a) 5,040

b) 10,080

c) 20,160

d) 40,320

Answer: d) 40,320

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

a) 60

b) 120

c) 240

d) 480

Answer: c) 240

A box contains 6 red balls, 4 green balls, and 3 blue balls. How many ways can 3 balls be drawn from the box, if order does not matter?

a) 15

b) 84

c) 104

d) 156

Answer: b) 84

How many ways can 4 different books be arranged on a shelf if 2 of the books must always be together?

a) 6

b) 12

c) 24

d) 48

Answer: b) 12

In how many ways can a president, vice president, and treasurer be chosen from a group of 10 people?

a) 30

b) 90

c) 120

d) 720

Answer: c) 120

A committee of 4 people is to be chosen from a group of 10. In how many ways can this be done?

a) 210

b) 240

c) 360

d) 504

Answer: a) 210

How many ways can 3 different books and 2 identical pens be arranged on a shelf?

a) 12

b) 24

c) 48

d) 60

Answer: b) 24

In how many ways can the letters of the word “BOOK” be arranged?

a) 4

b) 8

c) 12

d) 24

Answer: d) 24

How many ways can a 7-digit phone number be formed if the first digit cannot be 0 or 1, and repetition of digits is allowed?

a) 7,200,000

b) 8,000,000

c) 8,760,000

d) 9,999,999

Answer: c) 8,760,000

In how many ways can 6 students be seated in a row of chairs?

a) 120

b) 360

c) 720

d) 1,080

Answer: c) 720

How many ways can 3 boys and 3 girls be arranged in a line if the boys and girls must alternate?

a) 12

b) 24

c) 36

d) 48

Answer: b) 24

In how many ways can a committee of 4 people be chosen from a group of 8, where one person must be the chairperson?

a) 70

b) 84

c) 168

d) 280

Answer: c) 168

How many ways can the letters of the word “OPENAI” be arranged if the vowels must appear together?

a) 360

b) 720

c) 1,440

d) 2,880

Answer: c) 1,440

In how many ways can 3 boys and 3 girls be arranged in a row if all the boys must be together?

a) 120

b) 240

c) 360

d) 720

Answer: b) 240

How many ways can 4 books be arranged on a shelf if 2 books are identical?

a) 6

b) 12

c) 24

d) 48

Answer: a) 6

In how many ways can the letters of the word “COMPUTER” be arranged if the vowels must always be together?

a) 720

b) 1,440

c) 2,880

d) 5,760

Answer: b) 1,440

A box contains 5 red balls, 3 green balls, and 2 blue balls. How many ways can 4 balls be drawn from the box, if order does not matter?

a) 60

b) 84

c) 120

d) 150

Answer: b) 84

How many ways can a president, vice president, and treasurer be chosen from a group of 8 people?

a) 336

b) 480

c) 504

d) 720

Answer: a) 336

In how many ways can 5 students be seated in a circle?

a) 24

b) 60

c) 120

d) 240

Answer: c) 120