# Aptitude Questions: Permutations & Combinations Set 1

Hello Aspirants. Welcome to Online Reasoning Section in AffairsCloud.com. Here we are creating question sample in coded Permutations & Combinations, which is common for all the  competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

1. In a exam paper 1st section contains 10 questions each with 5 choices and  second section contains 5 questions each with 4 choices. In how many different ways can the paper be answered if all the questions are attempted.
A.105 × 45
B.510 × 45
C.510 × 54
D.105 × 54
E.None of these
Answer – B. 510 × 45
Explanation :
10 questions with 5 choices = 510
20 questions with 4 choices =  45
2. How many four digit number can be formed with the digits 5,9,1 and 3 only ?
A.64
B.216
C.256
D.324
E.None of these
Explanation :
4*4*4*4 = 256
3. Find the number of ways in which 9 students equally divided into three groups ?
A.280
B.360
C.200
D.540
E.None of these
Explanation :
9!/[3! ×(3!)3] = 362880/6*216 = 280
4. Find the number of ways of distributing 9 identical balls into 4 boxes so that no box is empty and each box being large enough to accommodate all balls ?
A.63
B.45
C.62
D.56
E.None of these
Explanation :
9-1 C 4-1  = 8 C 3 = 8*7*6/3*2*1 = 56
5. 12 students participated in  the competition and each get different score. In how many ways can three different prizes given ?
A.1320
B.1240
C.1650
D.1870
E.None of these
Explanation :
12*11*10 = 1320
6. How many arrangement can be made from the word COMMERCE, such that all the vowels do not come together ?
A.6800
B.5600
C.1080
D.9000
E.None of these
Explanation :
8 letters = 8!/ 2! 2! = 40320/4 = 10080
6 letters = 6!/2! = 360
Vowels = 3!/2! =  3
No of ways vowels together = 360*3 = 1080
No of ways vowels not together = 10080 – 1080 = 9000
7. Three brothers have 5 shirts, 8 pants and 6 ties. In how many ways can they wear them ?
A.2400200
B.2419000
C.2419200
D.2419100
E.None of these
Explanation :
5 P 3 *8 P 3*  6 P 3  = 60*336*120 = 2419200
8. 5 men and 3 women are to be seated such that no 2 women sit together and  2 men sit together. Find the no of ways in which this can be arranged ?
A.625
B.720
C.525
D.516
E.None of these
Explanation :
5!*3! = 120*6 = 720
9. A group consists of 3 couples  in which each of the 3 men have one wife each. In how many ways could they arranged in a straight line so that the men and women occupy alternate position ?
A.216
B.125
C.256
D.72
E.None of these
Explanation :
3!*3! + 3!*3! = 36+36 = 72
10. In how many ways can 5 different balls be distributed to 4 different boxes, when each of the can hold any no of ball ?
A.1024
B.1200
C.1234
D.1600
E.None of these