# AMCAT Previous Years Questions on Permutations and Combinations

 Topics Sub- Topics Expected Ques Basic Mathematics 6 – 8 Questions Applied Mathematics 8 – 10 Questions Engineering Mathematics 8 – 10 Questions

Question 1
How many groups of 6 persons can be formed from 8 men and 7 women?
A. 5000
B. 5005
C. 5050
D. None of these

Correct Op:B
Total no . of person = 8 + 7 = 15 No. of groups = 15C6 = 15! / {6! (15 – 6)!} = 15! / (6! 9!) = (15 x 14 x 13 x 12 x 11 x 10) / (6 x 5 x 4 x 3 x 2 x 1) = 5005

Question 2
8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of handshakes?
A. 16
B. 36
C. 56
D. 28

Correct Op:D
Required no. of hand shakes = {8 x (8 – 1)}/2 = 28

Question 3
Find the value of 5 P2.
A. 15
B. 18
C. 20
D. 122

Correct Op: C
5 P2 = 5! / (5 – 2)! = 5 x 4 = 20

Question 4
In how many different ways, can the letters of the word ‘INHALE’ be arranged?
A. 720
B. 360
C. 120
D. 650

Correct Op:A
The word ‘INHALE’ has 6 distinct letters. ∴ Number of arrangements = n ! = 6 ! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Question 5
In how many ways, the letters of the word ‘BANKING’ can be arranged?
A. 5040
B. 2540
C. 5080
D. 2520

Correct Op:D
Total letters = 7, but N has come twice. So, required number of arrangements = 7 ! / 2 ! = [7 x 6 x 5 x 4 x 3 x 2 ! ] / 2 ! = 2520

Question 6
In a meeting between two countries, each country has 12 delegates. All the delegates of one country shake hands with all delegates of the other country. Find the number of handshakes possible?
A. 72
B. 144
C.288
D. 234

Correct Op:B
Total number of handshakes = 12 x 12 = 144

Question 7
How many can straight lines be drawn from 15 non-collinear points?
A. 105
B. 120
C. 110
D. 115
E. 118

Correct Op:A

Question 8
If 56 Pr + 6 : 54 Pr + 3 = 30800 : 1 then the value of r is ?
A. 40
B. 41
C. 42
D. none

Correct Op: B
⇒ 56! / (50 – r)! = (30800 x 54!) / (51-r!) ⇒ 56 x 55 = 30800/(51 – r) ⇒ 51 – r = 10 ∴ r = 41

Question 9
There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed?
A. 2200
B. 2300
C. 2400
D. 3200

Correct Op: B
(25 x 24 x 23) / (1 x 2 x 3) = 2300