Permutations & Combinations
Q. How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
A.
5040
B.
10000
C.
9000
D.
7200
Show solution
Solution
The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.
Correct Answer: A — 5040
Learn More →
Q. How many different 4-digit PINs can be formed using the digits 0-9 without repetition?
A.
5040
B.
9000
C.
10000
D.
1000
Show solution
Solution
The number of 4-digit PINs is P(10, 4) = 5040.
Correct Answer: A — 5040
Learn More →
Q. How many different ways can 3 boys and 2 girls be seated in a row?
A.
30
B.
60
C.
120
D.
180
Show solution
Solution
The number of ways to arrange 5 people is 5! = 120.
Correct Answer: C — 120
Learn More →
Q. How many different ways can the letters of the word 'MATH' be arranged?
Show solution
Solution
The number of arrangements of the letters in 'MATH' is 4! = 24.
Correct Answer: B — 24
Learn More →
Q. How many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?
A.
100
B.
150
C.
200
D.
250
Show solution
Solution
The number of ways is 5C2 * 6C3 = 10 * 20 = 200.
Correct Answer: B — 150
Learn More →
Q. How many ways can 2 students be selected from a group of 5? (2019)
Show solution
Solution
The number of ways to select 2 students from 5 is given by 5C2 = 10.
Correct Answer: A — 10
Learn More →
Q. How many ways can 3 books be selected from a shelf of 10 books? (2022)
A.
120
B.
210
C.
100
D.
30
Show solution
Solution
The number of ways to select 3 books from 10 is given by 10C3 = 120.
Correct Answer: B — 210
Learn More →
Q. How many ways can 3 boys and 2 girls be seated in a row?
A.
30
B.
60
C.
120
D.
180
Show solution
Solution
The number of ways to arrange 5 people is 5! = 120.
Correct Answer: C — 120
Learn More →
Q. How many ways can 3 different colored balls be arranged in a row? (2022)
Show solution
Solution
The number of arrangements of 3 distinct balls is 3! = 6.
Correct Answer: A — 6
Learn More →
Q. How many ways can 3 different trophies be awarded to 5 students? (2022)
A.
60
B.
100
C.
120
D.
30
Show solution
Solution
The number of ways to award 3 trophies to 5 students is given by P(5,3) = 5! / (5-3)! = 60.
Correct Answer: C — 120
Learn More →
Q. How many ways can 3 out of 8 different colored balls be chosen? (2022)
Show solution
Solution
The number of ways to choose 3 balls from 8 is given by 8C3 = 56.
Correct Answer: A — 56
Learn More →
Q. How many ways can 3 prizes be awarded to 10 students if no student can win more than one prize?
A.
720
B.
1000
C.
1200
D.
100
Show solution
Solution
The number of ways to award 3 prizes is P(10, 3) = 720.
Correct Answer: A — 720
Learn More →
Q. How many ways can 3 students be selected from a group of 10?
A.
120
B.
90
C.
100
D.
80
Show solution
Solution
The number of ways to select 3 students from 10 is given by 10C3 = 120.
Correct Answer: A — 120
Learn More →
Q. How many ways can 4 different flags be arranged on a pole? (2021)
Show solution
Solution
The number of arrangements of 4 distinct flags is 4! = 24.
Correct Answer: A — 24
Learn More →
Q. How many ways can 4 different fruits be selected from 8 available fruits? (2021)
Show solution
Solution
The number of ways to choose 4 fruits from 8 is given by 8C4 = 70.
Correct Answer: A — 70
Learn More →
Q. How many ways can 4 different fruits be selected from 8?
Show solution
Solution
The number of ways to select 4 fruits from 8 is given by 8C4 = 70.
Correct Answer: B — 56
Learn More →
Q. How many ways can 4 different letters be chosen from the word 'COMPUTE'? (2022)
Show solution
Solution
The number of ways is 8C4 = 70.
Correct Answer: C — 56
Learn More →
Q. How many ways can 4 letters be chosen from the word 'COMBINATION'?
A.
210
B.
120
C.
150
D.
180
Show solution
Solution
The number of ways to choose 4 letters from 11 is 11C4 = 330.
Correct Answer: A — 210
Learn More →
Q. How many ways can 4 people be seated in a row of 6 chairs? (2021)
A.
360
B.
720
C.
240
D.
480
Show solution
Solution
The number of ways is 6P4 = 6! / (6-4)! = 360.
Correct Answer: A — 360
Learn More →
Q. How many ways can 4 prizes be distributed among 10 students if each student can receive at most one prize? (2019)
A.
5040
B.
720
C.
1000
D.
1200
Show solution
Solution
The number of ways to distribute 4 prizes among 10 students is 10P4 = 5040.
Correct Answer: A — 5040
Learn More →
Q. How many ways can 5 different letters be arranged if 2 letters are always together?
A.
48
B.
120
C.
240
D.
720
Show solution
Solution
Treat the 2 letters as one unit. So, we have 4 units to arrange: 4! * 2! = 48.
Correct Answer: C — 240
Learn More →
Q. How many ways can 5 different letters be arranged if 2 letters must always be together?
A.
60
B.
120
C.
240
D.
720
Show solution
Solution
Treat the 2 letters as one unit. So, we have 4 units to arrange: 4! * 2! = 48.
Correct Answer: C — 240
Learn More →
Q. How many ways can 6 different letters be arranged if 2 letters are always together?
A.
120
B.
240
C.
720
D.
1440
Show solution
Solution
Treat the 2 letters as one unit. So, we have 5 units to arrange: 5! = 120. The 2 letters can be arranged in 2! = 2 ways. Total = 120 * 2 = 240.
Correct Answer: D — 1440
Learn More →
Q. How many ways can 6 people be seated in a row? (2017)
A.
720
B.
600
C.
480
D.
360
Show solution
Solution
The number of arrangements of 6 people in a row is 6! = 720.
Correct Answer: A — 720
Learn More →
Q. How many ways can 7 different books be arranged on a shelf if 3 specific books must be together?
A.
720
B.
120
C.
5040
D.
840
Show solution
Solution
Treat the 3 specific books as one unit. So, we have 5 units to arrange: 5! * 3! = 360.
Correct Answer: C — 5040
Learn More →
Q. How many ways can 8 different books be arranged on a shelf if 3 specific books must be together?
A.
720
B.
5040
C.
40320
D.
2880
Show solution
Solution
Treat the 3 specific books as one unit. So, we have 6 units to arrange: 6! = 720. The 3 books can be arranged in 3! = 6 ways. Total = 720 * 6 = 4320.
Correct Answer: B — 5040
Learn More →
Q. How many ways can 8 different colored balls be arranged in a line?
A.
40320
B.
720
C.
1000
D.
100
Show solution
Solution
The number of arrangements is 8! = 40320.
Correct Answer: A — 40320
Learn More →
Q. How many ways can a committee of 4 be formed from 10 people? (2019)
A.
210
B.
120
C.
100
D.
30
Show solution
Solution
The number of ways to form a committee of 4 from 10 is given by 10C4 = 210.
Correct Answer: A — 210
Learn More →
Q. In how many ways can 3 prizes be awarded to 5 students? (2021)
A.
60
B.
100
C.
120
D.
80
Show solution
Solution
The number of ways to award 3 prizes to 5 students is 5P3 = 60.
Correct Answer: C — 120
Learn More →
Q. In how many ways can 4 different flags be arranged on a pole? (2015)
Show solution
Solution
The number of arrangements of 4 distinct flags is 4! = 24.
Correct Answer: A — 24
Learn More →
Showing 1 to 30 of 38 (2 Pages)
