Q. How many ways can 5 different letters be selected from the alphabet?
-
A.
26
-
B.
3003
-
C.
156
-
D.
120
Solution
The number of ways to choose 5 letters from 26 is C(26, 5) = 65780.
Correct Answer: B — 3003
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Q. How many ways can 5 different prizes be awarded to 3 students?
-
A.
60
-
B.
100
-
C.
150
-
D.
200
Solution
The number of ways to award 5 different prizes to 3 students is 3^5 = 243.
Correct Answer: C — 150
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Q. How many ways can 6 different books be arranged on a shelf if 2 specific books must be together?
-
A.
120
-
B.
720
-
C.
240
-
D.
480
Solution
Treat the 2 specific books as one unit. Then we have 5 units to arrange: 5! * 2! = 240.
Correct Answer: C — 240
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Q. How many ways can 6 people be arranged in a circle?
-
A.
720
-
B.
120
-
C.
60
-
D.
30
Solution
The number of arrangements in a circle is (n-1)! = (6-1)! = 5! = 120.
Correct Answer: A — 720
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Q. How many ways can 6 people be divided into 2 groups of 3?
Solution
The number of ways to divide 6 people into 2 groups of 3 is (6! / (3!3!)) / 2 = 20.
Correct Answer: A — 20
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Q. How many ways can a committee of 3 be formed from 5 people?
Solution
The number of ways to choose 3 from 5 is C(5,3) = 10.
Correct Answer: A — 10
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Q. How many ways can you arrange the letters of the word 'BANANA'?
Solution
The word 'BANANA' has 6 letters with 'A' repeating 3 times and 'N' repeating 2 times. The arrangements are 6!/(3!2!) = 60.
Correct Answer: B — 30
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Q. How many ways can you choose 3 fruits from a basket of 5 different fruits?
Solution
The number of ways to choose 3 fruits from 5 is given by 5C3 = 10.
Correct Answer: A — 10
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Q. How many ways can you form a committee of 3 from a group of 10 people?
-
A.
120
-
B.
90
-
C.
80
-
D.
100
Solution
The number of ways to form a committee of 3 from 10 is given by 10C3 = 120.
Correct Answer: A — 120
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Q. How many ways can you select 2 fruits from 5 different fruits?
Solution
The number of ways to choose 2 from 5 is given by 5C2 = 10.
Correct Answer: A — 10
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Q. How many ways can you select 2 students from a group of 8?
Solution
The number of ways to select 2 students from 8 is given by 8C2 = 28.
Correct Answer: A — 28
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Q. In how many ways can 3 boys and 2 girls be seated in a row?
Solution
The total number of arrangements is (3+2)! = 5! = 120.
Correct Answer: B — 60
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Q. In how many ways can 3 different colored balls be arranged in a line?
Solution
The number of arrangements of 3 different colored balls is 3! = 6.
Correct Answer: A — 6
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Q. In how many ways can 3 different colored balls be chosen from a set of 7?
Solution
The number of ways to choose 3 from 7 is given by C(7,3) = 7!/(3!4!) = 35.
Correct Answer: A — 35
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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 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 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 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 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 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 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 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 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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Q. In how many ways can 5 different objects be selected from 10 objects?
-
A.
252
-
B.
120
-
C.
10
-
D.
100
Solution
The number of ways to select 5 objects from 10 is 10C5 = 10! / (5! * 5!) = 252.
Correct Answer: A — 252
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Q. In how many ways can 6 different objects be selected and arranged in a line?
-
A.
720
-
B.
600
-
C.
840
-
D.
960
Solution
The number of arrangements of 6 different objects is 6! = 720.
Correct Answer: A — 720
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Q. In how many ways can 6 people be divided into 2 groups of 3?
Solution
The number of ways to divide 6 people into 2 groups of 3 is 6! / (3! * 3! * 2!) = 20.
Correct Answer: A — 20
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