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 fruits be arranged in a row?
Solution
The number of arrangements of 5 different fruits is 5! = 120.
Correct Answer: B — 120
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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 line?
-
A.
720
-
B.
120
-
C.
60
-
D.
30
Solution
The number of arrangements of 6 different colored balls is 6! = 720.
Correct Answer: A — 720
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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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Q. In how many ways can the letters of the word 'BOOK' be arranged? (2022)
Solution
The word 'BOOK' has 4 letters with 'O' repeating. The number of arrangements is 4! / 2! = 12.
Correct Answer: C — 16
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