# Aptitude Questions: Permutations & Combinations Set 5

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 !!

Questions Penned by Yogit

1. In how many ways can 5 boys and 4 girls can be seated in a row so that they are in alternate position.
a) 2780
b) 2880
c) 2800
d) 2980
e) None of these
Explanation :
First boys are seated in 5 position in 5! Ways, now remaining 4 places can be filled by 4 girls in 4! Ways, so number of ways = 5! 4! = 2880
2. In how many ways 5 African and five Indian can be seated along a circular table, so that they occupy alternate position.
a) 5! 5!
b) 4! 5!
c) 5! 4!
d) 4! 4!
Explanation :
First 5 African are seated along the circular table in (5-1)! Ways = 4!. Now Indian can be seated in 5! Ways, so 4! 5!
3. There is meeting of 20 delegates is to be held in a hotel. In how many ways these delegates can be seated along a round table, if three particular delegates always seat together.
a) 17! 3!
b) 18! 3!
c) 17! 4!
d) can’t be determined
Explanation :
Total 20 persons, 3 always seat together, 17 + 1 =18 delegates can be seated in (18 -1)! Ways = 17! And now that three can be arranged in 3! Ways. So, 17! 3!
4. In how many 8 prizes can be given to 3 boys, if all boys are equally eligible of getting the prize.
a) 512
b) 343
c) 256
d) 526
e) None of these
Explanation :
Prizes cab be given in 8*8*8 ways = 512 ways
5. There are 15 points in a plane out of which 6 are collinear. Find the number of lines that can be formed from 15 points.
a) 105
b) 90
c) 91
d) 95
e) None of these
Explanation :
From 15 points number of lines formed = 15c2
6 points are collinear, number of lines formed by these = 6c2
So total lines = 15c2 – 6c2 + 1 = 91
6. In party there is a total of 120 handshakes. If all the persons shakes hand with every other person. Then find the number of person present in the party.
a) 15
b) 16
c) 17
d) 18
e) None of these
Explanation :
Nc2 = 120 (N is the number of persons)
7. There are 8 boys and 12 girls in a class. 5 students have to be chosen for an educational trip. Find the number of ways in which this can be done if 2 particular girls are always included
a) 812
b) 816
c) 818
d) 820
e) None of these
Explanation :
18c3 = 816 (2 girls already selected)
8. In how many different ways the letters of the world INSIDE be arranged in such a way that all vowels always come together
a) 64
b) 72
c) 84
d) 96
e) None of these
Explanation :
Three vowels I, I and E can be arranged in 3!/2! Ways, remaining letters and group of vowels can be arranged in 4! Ways. So 4!*3!/2!
9. How many 3 digit number can be formed by 0, 2, 5, 3, 7 which is divisible by 5 and none of the digit is repeated.
a) 24
b) 36
c) 48
d) 60
e) None of these