PlacementPrepIn how many different ways can the letters of the word CAMPUS be arranged?
Solution
CAMPUS has 6 letters, all different.
Arrangements = 6! = 720.
Answer: (B) 720
Quantitative Aptitude · Counting
Permutations and Combinations: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
In how many ways can a committee of 2 men and 1 women be formed from 5 men and 7 women?
Solution
Choose men: C(5, 2) = 10. Choose women: C(7, 1) = 7.
Total = 10 × 7 = 70.
Answer: (D) 70
How many 4-digit numbers can be formed using the digits 1, 2, 4, 5, 6, 7, 8 if no digit is repeated?
Solution
First place: 7 choices, then 6, and so on for 4 places.
Total = P(7, 4) = 840.
Answer: (D) 840
In how many ways can 8 people sit in a row if 2 particular people must always sit together?
Solution
Treat the 2 people as one unit: 7 units can be arranged in 7! = 5040 ways.
Inside the unit, 2! = 2 ways. Total = 10080.
Answer: (D) 10,080
At a party, each of 18 people shakes hands once with every other person. How many handshakes are there?
Solution
Each handshake is a pair of people: C(18, 2) = 18 × 17/2 = 153.
Answer: (B) 153
In how many ways can 9 people be seated around a round table?
Solution
For a circular arrangement, fix one person; the rest can be arranged in (9 − 1)! = 40320 ways.
Answer: (B) 40,320
A team of 4 is chosen from 7 boys and 5 girls. In how many ways can it be chosen so that it has at least one girl?
Solution
All teams: C(12, 4) = 495. Teams with no girl: C(7, 4) = 35.
At least one girl = 495 − 35 = 460.
Answer: (D) 460
In how many different ways can the letters of the word DESIGN be arranged?
Solution
DESIGN has 6 letters, all different.
Arrangements = 6! = 720.
Answer: (B) 720
In how many ways can a committee of 2 men and 2 women be formed from 8 men and 6 women?
Solution
Choose men: C(8, 2) = 28. Choose women: C(6, 2) = 15.
Total = 28 × 15 = 420.
Answer: (D) 420
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated?
Solution
First place: 5 choices, then 4, and so on for 3 places.
Total = P(5, 3) = 60.
Answer: (A) 60
At a party, each of 24 people shakes hands once with every other person. How many handshakes are there?
Solution
Each handshake is a pair of people: C(24, 2) = 24 × 23/2 = 276.
Answer: (C) 276
In how many ways can 6 people be seated around a round table?
Solution
For a circular arrangement, fix one person; the rest can be arranged in (6 − 1)! = 120 ways.
Answer: (A) 120
A team of 4 is chosen from 7 boys and 6 girls. In how many ways can it be chosen so that it has at least one girl?
Solution
All teams: C(13, 4) = 715. Teams with no girl: C(7, 4) = 35.
At least one girl = 715 − 35 = 680.
Answer: (C) 680
In how many different ways can the letters of the word BALLOON be arranged?
Solution
BALLOON has 7 letters; L appears 2 times, O appears 2 times.
Arrangements = 7! / 2! / 2! = 1260.
Answer: (C) 1260
In how many ways can a committee of 2 men and 3 women be formed from 9 men and 4 women?
Solution
Choose men: C(9, 2) = 36. Choose women: C(4, 3) = 4.
Total = 36 × 4 = 144.
Answer: (D) 144
How many 3-digit numbers can be formed using the digits 2, 4, 5, 6, 7 if no digit is repeated?
Solution
First place: 5 choices, then 4, and so on for 3 places.
Total = P(5, 3) = 60.
Answer: (A) 60
At a party, each of 15 people shakes hands once with every other person. How many handshakes are there?
Solution
Each handshake is a pair of people: C(15, 2) = 15 × 14/2 = 105.
Answer: (C) 105
A team of 3 is chosen from 4 boys and 3 girls. In how many ways can it be chosen so that it has at least one girl?
Solution
All teams: C(7, 3) = 35. Teams with no girl: C(4, 3) = 4.
At least one girl = 35 − 4 = 31.
Answer: (D) 31
In how many different ways can the letters of the word SUCCESS be arranged?
Solution
SUCCESS has 7 letters; S appears 3 times, C appears 2 times.
Arrangements = 7! / 3! / 2! = 420.
Answer: (C) 420
In how many ways can a committee of 3 men and 1 women be formed from 5 men and 6 women?
Solution
Choose men: C(5, 3) = 10. Choose women: C(6, 1) = 6.
Total = 10 × 6 = 60.
Answer: (A) 60
How many 4-digit numbers can be formed using the digits 2, 3, 4, 6, 7, 9 if no digit is repeated?
Solution
First place: 6 choices, then 5, and so on for 4 places.
Total = P(6, 4) = 360.
Answer: (B) 360
In how many ways can 6 people sit in a row if 3 particular people must always sit together?
Solution
Treat the 3 people as one unit: 4 units can be arranged in 4! = 24 ways.
Inside the unit, 3! = 6 ways. Total = 144.
Answer: (A) 144
At a party, each of 17 people shakes hands once with every other person. How many handshakes are there?
Solution
Each handshake is a pair of people: C(17, 2) = 17 × 16/2 = 136.
Answer: (C) 136
In how many different ways can the letters of the word MANAGER be arranged?
Solution
MANAGER has 7 letters; A appears 2 times.
Arrangements = 7! / 2! = 2520.
Answer: (C) 2520
In how many ways can a committee of 3 men and 3 women be formed from 8 men and 4 women?
Solution
Choose men: C(8, 3) = 56. Choose women: C(4, 3) = 4.
Total = 56 × 4 = 224.
Answer: (B) 224
How many 4-digit numbers can be formed using the digits 4, 5, 6, 7, 9 if no digit is repeated?
Solution
First place: 5 choices, then 4, and so on for 4 places.
Total = P(5, 4) = 120.
Answer: (A) 120
In how many ways can 7 people sit in a row if 2 particular people must always sit together?
Solution
Treat the 2 people as one unit: 6 units can be arranged in 6! = 720 ways.
Inside the unit, 2! = 2 ways. Total = 1440.
Answer: (D) 1440
At a party, each of 20 people shakes hands once with every other person. How many handshakes are there?
Solution
Each handshake is a pair of people: C(20, 2) = 20 × 19/2 = 190.
Answer: (B) 190
In how many ways can 7 people be seated around a round table?
Solution
For a circular arrangement, fix one person; the rest can be arranged in (7 − 1)! = 720 ways.
Answer: (A) 720
In how many different ways can the letters of the word PEPPER be arranged?
Solution
PEPPER has 6 letters; P appears 3 times, E appears 2 times.
Arrangements = 6! / 3! / 2! = 60.
Answer: (B) 60
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