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