Q. How many subsets can be formed from the set {x, y, z, w, v}?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n = 5, so 2^5 = 32.
Correct Answer: A — 16
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Q. How many subsets does the set A = {a, b, c, d} have?
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Solution
The number of subsets of a set with n elements is given by 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.
Correct Answer: B — 8
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Q. How many subsets does the set A = {a, b, c} have?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n = 3, so the number of subsets is 2^3 = 8.
Correct Answer: D — 8
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Q. How many subsets does the set B = {a, b, c, d} have?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n=4, so the number of subsets is 2^4 = 16.
Correct Answer: B — 8
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Q. How many subsets does the set {a, b, c} have?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n = 3, so the number of subsets is 2^3 = 8.
Correct Answer: D — 8
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Q. How many subsets of the set H = {x, y} are there that do not contain the element y?
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Solution
The only subset that does not contain y is {∅} and {x}. Total = 2.
Correct Answer: A — 1
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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?
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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?
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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
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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
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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
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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
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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
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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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