Q. In how many ways can 3 different trophies be arranged on a shelf?
Solution
The number of arrangements is 3! = 6.
Correct Answer: A — 6
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Q. In how many ways can 3 men and 2 women be arranged in a line if the men must be together?
Solution
Treat the 3 men as one unit. So, we have 3 units (MMM, W, W). The arrangements = 3! * 3! = 36.
Correct Answer: B — 120
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Q. In how many ways can 3 prizes be awarded to 10 students?
-
A.
720
-
B.
1000
-
C.
120
-
D.
100
Solution
The number of ways to award 3 prizes to 10 students is 10P3 = 10! / (10-3)! = 720.
Correct Answer: A — 720
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Q. In how many ways can 3 prizes be awarded to 5 students? (2021)
-
A.
60
-
B.
100
-
C.
120
-
D.
80
Solution
The number of ways to award 3 prizes to 5 students is 5P3 = 60.
Correct Answer: C — 120
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Q. In how many ways can 3 prizes be distributed among 5 students? (2021)
-
A.
60
-
B.
100
-
C.
120
-
D.
80
Solution
The number of ways to distribute 3 prizes to 5 students is 5P3 = 60.
Correct Answer: C — 120
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Q. In how many ways can 3 red balls and 2 blue balls be arranged in a row?
Solution
The total arrangements = 5! / (3! * 2!) = 10.
Correct Answer: A — 10
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Q. In how many ways can 3 red, 2 blue, and 1 green balls be arranged in a line?
Solution
The total arrangements = 6! / (3! * 2! * 1!) = 60.
Correct Answer: B — 120
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Q. In how many ways can 3 students be chosen from a group of 8? (2015)
Solution
The number of ways to choose 3 students from 8 is 8C3 = 56.
Correct Answer: A — 56
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Q. In how many ways can 3 students be selected from a class of 8 to represent in a competition?
Solution
The number of ways to choose 3 students from 8 is given by 8C3 = 56.
Correct Answer: A — 56
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Q. In how many ways can 4 different books be arranged on a shelf?
Solution
The number of arrangements of 4 different books is 4! = 24.
Correct Answer: B — 24
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Q. In how many ways can 4 different books be chosen from a shelf of 10 books?
-
A.
210
-
B.
120
-
C.
240
-
D.
300
Solution
The number of ways to choose 4 books from 10 is C(10, 4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 4 different books be selected from a shelf of 10 books?
-
A.
210
-
B.
120
-
C.
240
-
D.
300
Solution
The number of ways to choose 4 books from 10 is C(10,4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 4 different colored balls be arranged in a line?
Solution
The number of arrangements is 4! = 24.
Correct Answer: B — 24
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Q. In how many ways can 4 different colored balls be placed in 3 different boxes?
Solution
Each ball can go into any of the 3 boxes, so the total ways = 3^4 = 81.
Correct Answer: A — 81
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Q. In how many ways can 4 different flags be arranged on a pole? (2015)
Solution
The number of arrangements of 4 distinct flags is 4! = 24.
Correct Answer: A — 24
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Q. In how many ways can 4 different fruits be selected from 10 fruits?
-
A.
210
-
B.
120
-
C.
240
-
D.
300
Solution
The number of ways to choose 4 fruits from 10 is C(10, 4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 4 different letters be arranged?
Solution
The number of arrangements is 4! = 24.
Correct Answer: A — 24
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Q. In how many ways can 4 different prizes be awarded to 3 students?
Solution
The number of ways is P(4, 3) = 4! / 1! = 24.
Correct Answer: C — 36
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Q. In how many ways can 4 different prizes be distributed among 10 students? (2023)
-
A.
5040
-
B.
10000
-
C.
2400
-
D.
120
Solution
The number of ways to distribute 4 different prizes among 10 students is 10P4 = 5040.
Correct Answer: A — 5040
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Q. In how many ways can 4 different prizes be distributed among 3 students?
Solution
Each prize can go to any of the 3 students, so the total ways = 3^4 = 81.
Correct Answer: A — 81
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Q. In how many ways can 4 prizes be distributed among 10 students?
-
A.
210
-
B.
5040
-
C.
10000
-
D.
1001
Solution
The number of ways to distribute 4 prizes among 10 students is 10P4 = 5040.
Correct Answer: B — 5040
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Q. In how many ways can 4 students be seated in a row of 6 chairs? (2021)
-
A.
360
-
B.
720
-
C.
120
-
D.
240
Solution
Choose 4 chairs from 6 (6C4) and arrange 4 students (4!). Total = 15 * 24 = 360.
Correct Answer: B — 720
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Q. In how many ways can 4 students be selected from a group of 10?
-
A.
210
-
B.
120
-
C.
240
-
D.
300
Solution
The number of ways to select 4 students from 10 is C(10,4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 5 different books be arranged on a shelf? (2021)
-
A.
60
-
B.
120
-
C.
240
-
D.
720
Solution
The number of arrangements of 5 distinct books is 5! = 120.
Correct Answer: D — 720
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Q. In how many ways can 5 different colored balls be arranged in a box?
-
A.
60
-
B.
120
-
C.
100
-
D.
80
Solution
The number of arrangements is 5! = 120.
Correct Answer: B — 120
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Q. In how many ways can 5 different colored balls be arranged in a line?
-
A.
60
-
B.
120
-
C.
240
-
D.
720
Solution
The number of ways to arrange 5 different colored balls is 5! = 120.
Correct Answer: D — 720
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Q. In how many ways can 5 different colored balls be arranged in a row? (2021)
-
A.
120
-
B.
60
-
C.
100
-
D.
80
Solution
The number of arrangements of 5 different colored balls is 5! = 120.
Correct Answer: A — 120
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Q. In how many ways can 5 different flags be arranged on a pole?
Solution
The number of arrangements of 5 different flags is 5! = 120.
Correct Answer: A — 120
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Q. In how many ways can 5 different fruits be arranged in a row?
Solution
The number of arrangements of 5 different fruits is 5! = 120.
Correct Answer: B — 120
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Q. In how many ways can 5 different items be selected from 10 items?
-
A.
252
-
B.
120
-
C.
200
-
D.
300
Solution
The number of ways to select 5 items from 10 is C(10, 5) = 252.
Correct Answer: A — 252
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