How many 3-digit even numbers can be formed from the digits 1, 2, 6, 7, 9 without repetition?
Solution
The units digit must be even: 2 choices (2, 6).
The other two places: P(4, 2) = 12. Total = 2 × 12 = 24.
Answer: (B) 24
Quantitative Aptitude · Counting and probability
Permutations and Combinations: MAH CET, NMAT and SNAP practice questions
20 questions in the pattern of MAH MBA CET, NMAT and SNAP. Each question is marked with the exams it suits. Answer it, then open the step-by-step solution.
Exam:
A team of 4 is to be 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.
Answer = 460.
Answer: (A) 460
A team of 3 is to be chosen from 6 boys and 6 girls. In how many ways can it be chosen so that it has at least one girl?
Solution
All teams: C(12, 3) = 220. Teams with no girl: C(6, 3) = 20.
Answer = 200.
Answer: (B) 200
On a grid, how many shortest paths are there from one corner to the opposite corner of a 5 × 5 rectangle of squares (moving only right or up)?
Solution
Every shortest path has 5 rights and 5 ups in some order.
Number = C(10, 5) = 252.
Answer: (D) 252
How many straight lines can be drawn through 11 points, no three of which are on the same line?
Solution
Each line is fixed by 2 points: C(11, 2) = 55.
Answer: (D) 55
In how many ways can 5 players be chosen from 12 if one particular player must always be included?
Solution
He is already chosen; choose 4 more from 11: 330.
Answer: (A) 330
In how many ways can the letters of the word MANAGER be arranged so that the vowels always come together?
Solution
Vowels AAE form one block. Arrange the block with MNGR: 5! = 120.
Arrange the vowels inside: 3!/2! = 3.
Total = 120 × 3 = 360.
Answer: (D) 360
In how many ways can the letters of the word APPLE be arranged so that the vowels always come together?
Solution
Vowels AE form one block. Arrange the block with PPL: 4!/2! = 12.
Arrange the vowels inside: 2! = 2.
Total = 12 × 2 = 24.
Answer: (C) 24
In how many ways can a committee of 3 men and 2 women be formed from 7 men and 5 women?
Solution
C(7, 3) × C(5, 2) = 35 × 10 = 350.
Answer: (C) 350
In how many ways can the letters of the word SCHOOL be arranged?
Solution
SCHOOL has 6 letters with repeats O × 2.
Arrangements = 6!/2! = 360.
Answer: (D) 360
From 4 consonants and 3 vowels, how many words of 2 consonants and 2 vowels can be formed (letters not repeated)?
Solution
Choose letters: C(4, 2) × C(3, 2) = 18.
Arrange the 4 chosen letters: 4! = 24. Total = 432.
Answer: (B) 432
In how many ways can a committee of 3 men and 2 women be formed from 5 men and 6 women?
Solution
C(5, 3) × C(6, 2) = 10 × 15 = 150.
Answer: (B) 150
In how many ways can the letters of the word BANANA be arranged?
Solution
BANANA has 6 letters with repeats A × 3, N × 2.
Arrangements = 6!/3!/2! = 60.
Answer: (B) 60
In a tournament, each of 12 teams plays every other team twice. How many matches are played?
Solution
Pairs of teams: C(12, 2) = 66. Each pair plays twice: × 2.
Matches = 132.
Answer: (B) 132
In how many ways can 6 people sit around a round table if two particular people must sit together?
Solution
Treat the pair as one: (5 − 1)! = 24 circular arrangements; the pair can swap: × 2.
Total = 48.
Answer: (D) 48
How many 4-digit numbers can be formed from the digits 2, 3, 4, 5, 7, 9 if no digit is repeated?
Solution
P(6, 4) = 360.
Answer: (D) 360
How many 3-digit numbers can be formed from the digits 1, 2, 5, 6, 7, 8 if no digit is repeated?
Solution
P(6, 3) = 120.
Answer: (C) 120
How many 3-digit even numbers can be formed from the digits 2, 3, 4, 5, 8 without repetition?
Solution
The units digit must be even: 3 choices (2, 4, 8).
The other two places: P(4, 2) = 12. Total = 3 × 12 = 36.
Answer: (B) 36
In how many ways can 7 people sit in a row if 3 particular people must always sit together?
Solution
Treat the 3 as one unit: 5! = 120 ways; inside: 3! = 6.
Total = 720.
Answer: (D) 720
If all the arrangements of the letters of the word HOME are written in dictionary order, what is the rank of the word HOME?
Solution
Count the arrangements that come before HOME letter by letter, using the letters in alphabetical order (EHMO).
11 arrangements come before it, so its rank is 12.
Answer: (B) 12
These are original practice questions written by Target Campus in the pattern and difficulty of MAH MBA CET, NMAT, SNAP and other MBA entrance tests. They are not previous-year papers.
Preparing for MAH CET, NMAT, SNAP or CAT? Courses, live classes and mocks by Dr. Kiran Derle at Target Campus.
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