Q. How many ways can 3 different colored balls be arranged in a row? (2022)
Solution
The number of arrangements of 3 distinct balls is 3! = 6.
Correct Answer: A — 6
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Q. How many ways can 3 different fruits be chosen from 8 fruits?
Solution
The number of ways is C(8,3) = 56.
Correct Answer: B — 84
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Q. How many ways can 3 different fruits be selected from 5 available fruits?
Solution
The number of ways to choose 3 from 5 is given by 5C3 = 10.
Correct Answer: B — 15
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Q. How many ways can 3 different gifts be given to 5 children if each child can receive more than one gift? (2022)
-
A.
125
-
B.
243
-
C.
60
-
D.
30
Solution
Each gift can go to any of the 5 children, so the total ways = 5^3 = 125.
Correct Answer: B — 243
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Q. How many ways can 3 different letters be chosen from the word 'COMBINATION'?
-
A.
120
-
B.
220
-
C.
60
-
D.
80
Solution
The number of ways is C(11, 3) = 165.
Correct Answer: C — 60
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Q. How many ways can 3 different trophies be awarded to 5 students? (2022)
-
A.
60
-
B.
100
-
C.
120
-
D.
30
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
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Q. How many ways can 3 letters be chosen from the word 'COMBINATION'?
Solution
The number of ways to choose 3 letters from 11 distinct letters is 11C3 = 165.
Correct Answer: B — 60
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Q. 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). Arrangements = 4! * 3! = 24 * 6 = 144.
Correct Answer: B — 120
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Q. How many ways can 3 out of 8 different colored balls be chosen? (2022)
Solution
The number of ways to choose 3 balls from 8 is given by 8C3 = 56.
Correct Answer: A — 56
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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
Solution
The number of ways to award 3 prizes is P(10, 3) = 720.
Correct Answer: A — 720
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Q. How many ways can 3 red balls and 2 blue balls be arranged in a row?
Solution
The arrangements = 5! / (3! * 2!) = 10.
Correct Answer: A — 10
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Q. How many ways can 3 red, 2 blue, and 1 green balls be arranged in a line?
Solution
The arrangements = 6! / (3! * 2! * 1!) = 60.
Correct Answer: A — 60
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Q. How many ways can 3 red, 2 blue, and 1 green balls be arranged in a row?
Solution
The total arrangements = 6! / (3! * 2! * 1!) = 60.
Correct Answer: A — 60
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Q. How many ways can 3 students be selected from a group of 10?
-
A.
120
-
B.
90
-
C.
100
-
D.
80
Solution
The number of ways to select 3 students from 10 is given by 10C3 = 120.
Correct Answer: A — 120
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Q. 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. 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. 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. How many ways can 4 different flags be arranged on a pole? (2021)
Solution
The number of arrangements of 4 distinct flags is 4! = 24.
Correct Answer: A — 24
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Q. How many ways can 4 different fruits be selected from 8 available fruits? (2021)
Solution
The number of ways to choose 4 fruits from 8 is given by 8C4 = 70.
Correct Answer: A — 70
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Q. How many ways can 4 different fruits be selected from 8?
Solution
The number of ways to select 4 fruits from 8 is given by 8C4 = 70.
Correct Answer: B — 56
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Q. How many ways can 4 different fruits be selected from a basket of 10 fruits?
-
A.
210
-
B.
120
-
C.
300
-
D.
150
Solution
The number of ways to choose 4 fruits from 10 is given by 10C4 = 210.
Correct Answer: A — 210
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Q. How many ways can 4 different letters be chosen from the word 'COMBINATION'?
-
A.
210
-
B.
126
-
C.
70
-
D.
84
Solution
The number of ways to choose 4 letters from 11 distinct letters is 11C4 = 330.
Correct Answer: A — 210
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Q. How many ways can 4 different letters be chosen from the word 'COMPUTE'? (2022)
Solution
The number of ways is 8C4 = 70.
Correct Answer: C — 56
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Q. How many ways can 4 different letters be selected from the word 'COMBINATION'?
-
A.
210
-
B.
120
-
C.
60
-
D.
30
Solution
The number of ways to choose 4 letters from 11 distinct letters is 11C4 = 330.
Correct Answer: A — 210
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Q. How many ways can 4 different prizes be awarded to 3 students?
Solution
The number of ways to award 4 different prizes to 3 students is 3^4 = 81.
Correct Answer: C — 36
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Q. 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. How many ways can 4 letters be chosen from the word 'COMBINATION'?
-
A.
210
-
B.
120
-
C.
150
-
D.
180
Solution
The number of ways to choose 4 letters from 11 is 11C4 = 330.
Correct Answer: A — 210
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Q. How many ways can 4 people be seated in a row of 6 chairs? (2021)
-
A.
360
-
B.
720
-
C.
240
-
D.
480
Solution
The number of ways is 6P4 = 6! / (6-4)! = 360.
Correct Answer: A — 360
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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
Solution
The number of ways to distribute 4 prizes among 10 students is 10P4 = 5040.
Correct Answer: A — 5040
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Q. How many ways can 4 students be selected from a class of 10? (2020)
-
A.
210
-
B.
120
-
C.
240
-
D.
300
Solution
The number of ways to choose 4 students from 10 is given by 10C4 = 210.
Correct Answer: A — 210
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