# Permutations and Combinations mcq

### Permutations and Combinations mcq

How many ways can the letters of the word “APPLE” be arranged?
a) 5
b) 10
c) 15
d) 20

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

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

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

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

How many ways can 4 books be arranged on a shelf?
a) 12
b) 16
c) 20
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

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

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

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

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

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

How many ways can 3 different books and 2 identical pens be arranged on a shelf?
a) 12
b) 24
c) 48
d) 60

In how many ways can the letters of the word “BOOK” be arranged?
a) 4
b) 8
c) 12
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

In how many ways can 6 students be seated in a row of chairs?
a) 120
b) 360
c) 720
d) 1,080

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

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

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

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

How many ways can 4 books be arranged on a shelf if 2 books are identical?
a) 6
b) 12
c) 24
d) 48

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

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

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