Q. From a group of 10 people, how many ways can a committee of 4 be formed?
A.
210
B.
120
C.
150
D.
180
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Solution
The number of ways to choose 4 people from 10 is given by 10C4 = 210.
Correct Answer: A — 210
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Q. From a set of 8 different books, how many ways can you choose 3 books?
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Solution
The number of ways to choose 3 books from 8 is given by 8C3 = 56.
Correct Answer: B — 84
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Q. How many different ways can 3 red, 2 blue, and 1 green balls be arranged in a line?
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Solution
The total arrangements = 6! / (3! * 2! * 1!) = 60.
Correct Answer: B — 120
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Q. How many different ways can 4 people be seated at a round table?
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Solution
The number of arrangements of n people at a round table is (n-1)!. For 4 people, it is 3! = 6.
Correct Answer: B — 12
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Q. How many different ways can 4 students be selected from a group of 10?
A.
210
B.
120
C.
100
D.
90
Show solution
Solution
The number of ways to choose 4 from 10 is given by 10C4 = 210.
Correct Answer: A — 210
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Q. How many different ways can 6 people be seated at a round table?
A.
720
B.
120
C.
600
D.
480
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Solution
The number of arrangements of 6 people at a round table is (6-1)! = 5! = 120.
Correct Answer: A — 720
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Q. How many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?
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Solution
The number of ways = 5C2 * 4C2 = 10 * 6 = 60.
Correct Answer: A — 60
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Q. How many ways can 2 boys and 2 girls be selected from 6 boys and 4 girls?
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Solution
The number of ways is C(6,2) * C(4,2) = 15 * 6 = 90.
Correct Answer: A — 60
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Q. How many ways can 3 different books be chosen from a set of 7 books?
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Solution
The number of ways to choose 3 books from 7 is 7C3 = 7! / (3! * 4!) = 35.
Correct Answer: A — 35
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Q. How many ways can 3 different fruits be chosen from 8 fruits?
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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?
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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 letters be chosen from the word 'COMBINATION'?
A.
120
B.
220
C.
60
D.
80
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Solution
The number of ways is C(11, 3) = 165.
Correct Answer: C — 60
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Q. How many ways can 3 letters be chosen from the word 'COMBINATION'?
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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?
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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 red balls and 2 blue balls be arranged in a row?
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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?
Show solution
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?
Show solution
Solution
The total arrangements = 6! / (3! * 2! * 1!) = 60.
Correct Answer: A — 60
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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
Show solution
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?
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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?
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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 fruits be selected from a basket of 10 fruits?
A.
210
B.
120
C.
300
D.
150
Show solution
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
Show solution
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 selected from the word 'COMBINATION'?
A.
210
B.
120
C.
60
D.
30
Show solution
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?
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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?
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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 students be selected from a group of 10?
A.
210
B.
120
C.
150
D.
180
Show solution
Solution
The number of ways is C(10, 4) = 210.
Correct Answer: A — 210
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Q. How many ways can 5 different books be arranged on a shelf?
A.
60
B.
120
C.
100
D.
80
Show solution
Solution
The number of arrangements of 5 different books is 5! = 120.
Correct Answer: B — 120
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Q. How many ways can 5 different books be selected from a shelf of 10 books?
A.
252
B.
120
C.
200
D.
300
Show solution
Solution
The number of ways is C(10, 5) = 252.
Correct Answer: A — 252
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Q. How many ways can 5 different letters be arranged such that two specific letters are never together?
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Solution
Total arrangements = 5! = 120. Arrangements with the two letters together = 4! * 2! = 48. So, arrangements where they are not together = 120 - 48 = 72.
Correct Answer: C — 72
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Q. How many ways can 5 different letters be arranged such that two specific letters are always together?
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Solution
Treat the two specific letters as one unit. Then, we have 4 units to arrange: 4! = 24. The two letters can be arranged in 2! = 2 ways. Total = 24 * 2 = 48.
Correct Answer: B — 60
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