Permutations & Combinations
Q. How many ways can 7 different books be arranged on a shelf if 3 specific books must be together?
-
A.
720
-
B.
120
-
C.
5040
-
D.
840
Solution
Treat the 3 specific books as one unit. So, we have 5 units to arrange: 5! * 3! = 360.
Correct Answer: C — 5040
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Q. How many ways can 8 different books be arranged on a shelf if 3 specific books must be together?
-
A.
720
-
B.
5040
-
C.
40320
-
D.
2880
Solution
Treat the 3 specific books as one unit. So, we have 6 units to arrange: 6! = 720. The 3 books can be arranged in 3! = 6 ways. Total = 720 * 6 = 4320.
Correct Answer: B — 5040
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Q. How many ways can 8 different colored balls be arranged in a line?
-
A.
40320
-
B.
720
-
C.
1000
-
D.
100
Solution
The number of arrangements is 8! = 40320.
Correct Answer: A — 40320
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Q. How many ways can a committee of 4 be formed from 10 people? (2019)
-
A.
210
-
B.
120
-
C.
100
-
D.
30
Solution
The number of ways to form a committee of 4 from 10 is given by 10C4 = 210.
Correct Answer: A — 210
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Q. How many ways can a committee of 4 be formed from 8 people? (2019)
Solution
The number of ways to form a committee of 4 from 8 is 8C4 = 70.
Correct Answer: A — 70
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Q. In how many ways can 3 different colored balls be arranged in a row? (2015)
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 fruits be selected from a basket of 7 fruits? (2014)
Solution
The number of ways to select 3 from 7 is C(7, 3) = 35.
Correct Answer: A — 35
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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 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 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 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 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 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 letters be arranged if 2 letters are always together? (2019)
Solution
Treat the 2 letters as one unit. So, we have 4 units to arrange: 4! * 2! = 48.
Correct Answer: B — 60
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Q. In how many ways can 6 different colored balls be arranged in a row? (2018)
-
A.
720
-
B.
600
-
C.
480
-
D.
360
Solution
The number of arrangements of 6 distinct balls is 6! = 720.
Correct Answer: A — 720
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Q. In how many ways can 6 people be seated in a row?
-
A.
720
-
B.
600
-
C.
480
-
D.
360
Solution
The number of arrangements of 6 people is 6! = 720.
Correct Answer: A — 720
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Q. In how many ways can 7 people be divided into 3 groups if one group must have 3 people?
-
A.
210
-
B.
300
-
C.
420
-
D.
560
Solution
Choose 3 people from 7: C(7, 3) = 35. The remaining 4 can be divided into 2 groups in 2 ways. Total = 35 * 2 = 70.
Correct Answer: B — 300
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