Permutation and Combination
Q. How many ways can the letters of the word 'BANANA' be arranged?
Solution
The number of arrangements is 6! / (3!) = 20.
Correct Answer: B — 30
Q. In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?
Solution
The number of ways to select 2 boys from 5 is C(5, 2) and 2 girls from 4 is C(4, 2). Total = C(5, 2) * C(4, 2) = 10 * 6 = 60.
Correct Answer: A — 60
Q. In how many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?
-
A.
100
-
B.
120
-
C.
150
-
D.
200
Solution
The number of ways is C(5,2) * C(6,3) = 10 * 20 = 200.
Correct Answer: B — 120
Q. In how many ways can 2 out of 5 different fruits be selected?
Solution
The number of ways to choose 2 fruits from 5 is C(5, 2) = 10.
Correct Answer: A — 10
Q. In how many ways can 3 different prizes be awarded to 5 students?
Solution
The number of ways to award 3 different prizes to 5 students is P(5, 3) = 5! / (5-3)! = 60.
Correct Answer: A — 60
Q. In how many ways can 3 different trophies be awarded to 10 students?
-
A.
720
-
B.
1000
-
C.
120
-
D.
300
Solution
The number of ways to award 3 trophies to 10 students is 10P3 = 720.
Correct Answer: A — 720
Q. In how many ways can 3 students be selected from a group of 10?
-
A.
120
-
B.
90
-
C.
100
-
D.
80
Solution
The number of ways to choose 3 students from 10 is C(10, 3) = 120.
Correct Answer: A — 120
Q. In how many ways can 4 different colored balls be arranged in a row?
Solution
The number of arrangements is 4! = 24.
Correct Answer: B — 24
Q. In how many ways can 4 different prizes be awarded to 10 students?
-
A.
5040
-
B.
720
-
C.
100
-
D.
40
Solution
The number of ways to award 4 different prizes to 10 students is P(10, 4) = 10! / (10-4)! = 5040.
Correct Answer: A — 5040
Q. In how many ways can 4 people be seated at a round table?
Solution
The number of arrangements of 4 people at a round table is (4-1)! = 6.
Correct Answer: B — 12
Q. In how many ways can 5 books be arranged on a shelf?
Solution
The number of ways to arrange 5 books is 5! = 120.
Correct Answer: A — 120
Q. In how many ways can 5 different books be arranged on a shelf if 2 specific books must be together?
Solution
Treat the 2 specific books as one unit. Then, we have 4 units to arrange: 4! × 2! = 48.
Correct Answer: A — 48
Q. In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be displayed at a time?
Solution
The number of ways to select and arrange 3 books from 5 is 5P3 = 60.
Correct Answer: A — 60
Q. In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be placed?
Solution
The number of ways to select and arrange 3 books from 5 is P(5, 3) = 5! / (5-3)! = 60.
Correct Answer: B — 120
Q. In how many ways can 5 different prizes be distributed among 3 students?
-
A.
243
-
B.
125
-
C.
60
-
D.
30
Solution
The number of ways to distribute 5 different prizes among 3 students is 3^5 = 243.
Correct Answer: A — 243
Q. In how many ways can 5 different trophies be awarded to 3 students?
Solution
The number of ways to award 5 trophies to 3 students is 3^5 = 243.
Correct Answer: A — 60
Q. In 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.
60
Solution
Treat the 2 specific books as one unit. Then, we have 5 units to arrange: 5! = 120. The 2 books can be arranged in 2! = 2 ways. Total = 120 * 2 = 240.
Correct Answer: B — 720
Q. In how many ways can 6 people be seated around a circular table?
-
A.
720
-
B.
120
-
C.
60
-
D.
30
Solution
The number of ways to arrange 6 people around a circular table is (6-1)! = 5! = 120.
Correct Answer: B — 120
Q. In how many ways can 6 people be seated at a round table?
-
A.
120
-
B.
720
-
C.
60
-
D.
30
Solution
The number of ways to arrange 6 people at a round table is (6-1)! = 5! = 120.
Correct Answer: A — 120
Q. In how many ways can 6 people be seated in a round table?
-
A.
720
-
B.
120
-
C.
60
-
D.
30
Solution
The number of ways to arrange 6 people in a round table is (6-1)! = 5! = 120.
Correct Answer: A — 720
Q. In how many ways can 7 different books be arranged if 3 specific books must be on the top?
-
A.
720
-
B.
120
-
C.
5040
-
D.
840
Solution
The 3 specific books can be arranged in 3! = 6 ways. The remaining 4 books can be arranged in 4! = 24 ways. Total = 6 * 24 = 144.
Correct Answer: A — 720
Q. In how many ways can 7 different books be arranged on a shelf if 3 specific books must be in the middle?
-
A.
720
-
B.
1440
-
C.
5040
-
D.
840
Solution
Arrange the 3 specific books in the middle (3!) and the remaining 4 books (4!): 3! * 4! = 1440.
Correct Answer: B — 1440
Q. In how many ways can the letters of the word 'BANANA' be arranged?
Solution
The number of arrangements of the letters in 'BANANA' is 6! / (3!) = 20.
Correct Answer: B — 30
Q. In how many ways can the letters of the word 'MATH' be arranged?
Solution
The number of ways to arrange the letters of 'MATH' is 4! = 24.
Correct Answer: A — 24
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