aptitude : : permutation and combination
 
@ : Home  >  Aptitude  >  permutation and combination  >   Questions & Answers
 
Overview
Important Formulas
  Exercise
   Exercise 2
   Exercise 3
   Exercise 1
1.
There are 5 members in a delegation which is to be sent abroad.
The total no. of members is 10. In how many ways can the selection be made so that a particular member is always (i) included (ii) excluded?
 
A.
126 , 126

B.

124, 126
C.
126,124
D.
124,124
   
  Answer Discuss in Forum Calculator Workspace
Answer: A
Explanation :
Selection of one particular member can be done in 1C1 = 1 way.
 
After the selection of the particular member, we are left with 9 members and for the delegation, we need 4 members more. So selection can be done in 9C4ways.
 
Reqd no. ofways of selection= 1C1/ 9C4 = 1X 9 X 8 X 7 X 6/24 = 126
(ii) When one particular person has to be always excluded from the
5-member delegation, we are left with 10 - 1 = 9 persons. So selection can be done in 9C
ways.
:.Reqd no.= 9C5 = 126
 
 






 
2.
In a party every person shakes hand with every other person. If there was a total of 210 handshakes in the party, find the no. of persons who were present in the party.
 
A.
20

B.

22
C.
21
D.
24
   
  Answer Discuss in Forum Calculator Workspace
Answer: C
Explanation :
For each selection of two persons there will be one handshake. So,
no. of handshakes in the party = nC2 , where n = no. of persons.
 
Now, nC2 = 210 (given)
so, n = 21
 






 
3.
How many 4letter code can be formed using the first 9 letters of the English alphabets, if no letter can be repeated?
 
A.
3024

B.

3036
C.
3021
D.
3034
   
  Answer Discuss in Forum Calculator Workspace
Answer: A
Explanation :
By fundamental principle, it is (9 x 8 x 7 x 6) ways
 
= 3024ways






 
4.
5 children are to be seated on a bench. In how many ways can it be done if the eldest child always sits in the middle?
 
A.
48

B.

12
C.
36
D.
24
   
  Answer Discuss in Forum Calculator Workspace
Answer: D
Explanation :
Here, the eldest child always sits in the middle . Total number of remaining seats = (5- 1) = 4 seats and the total number  of remaining children = 4
So, by fundamental  principle , we  get total arrangements
= (4 x 3 x 2 x 1) ways = 24 ways
Or 4 p4  = 4!/(4-4)! = 24 ways






 
5.
5 children are to be seated on one bench. In how many ways can it be done?
 
A.
120

B.

140
C.
124
D.
144
   
  Answer Discuss in Forum Calculator Workspace
Answer: A
Explanation :






 
6.
In how many ways can 3 people be seated in a row containing 6 seats?
 
A.
110

B.

130
C.
140
D.
120
   
  Answer Discuss in Forum Calculator Workspace
Answer: D
Explanation :
1st person can be seated in 6 ways, 2nd person in 5 ways, 3rd person in 4 ways
Then the total no.of ways = 6 x 5 x 4 = 120 ways






 
7.
Find the no. ofways in which 4 identical balls can be distributed among 6 identical boxes, if not more than one ball goes into a box?
 
A.
12

B.

6
C.
4
D.
15
   
  Answer Discuss in Forum Calculator Workspace
Answer: D
Explanation :
No. of identical balls= 4 and no. of identical boxes= 6
Now, distributing 4 identical balls among 6 identical boxes when not more than one ball goes into a box, implies to select 4 boxes from among the 6 boxes, whicl: can be done in 6C4 = 6!/4!x2! = 15 ways






 
8.
How many words can be formed out of the letters of the word BANANA so that the consonants occupy the even places?
 
A.
6

B.

36
C.
12
D.
3
   
  Answer Discuss in Forum Calculator Workspace
Answer: D
Explanation :

1    2    3    4    5    6

The word BANANA contains 6 letters out of which A occurs thrice and N occurs twice.
The 3 consonants 8 and N (which occurs twice) can be arranged 3 at the 3 even places 2, 4 and 6 in 3!/2! = 3 ways
The remaining 3 odd places can be arranged with triple A in 3!/3! = 1 way
so, required number = 3 x 1 = 3 ways
 
 

 







 
9.
A man wants to go abroad by ship and return by air. He has a choice of 4 ships to go and 5 airlines to return. In how many ways can man perform his journey?
 
A.
20

B.

18
C.
24
D.
16
   
  Answer Discuss in Forum Calculator Workspace
Answer: A
Explanation :
No.of choices to go by ship = 5
No.of choices to return by airlines = 4
From the fundamental principle, total no.of ways = 5 x 4 = 20






 
10.
There are 5 routes from place A to B and 2 routes from place B to C. Find how many routes are there from place A to C via B?
 
A.
7

B.

10
C.
8
D.
12
   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :
No.of routes from A to B = 5
No.of routes from B to C = 2
From the fundamental principle, total n.of routes from A to C via B = 5 x 2 = 10






 

Pages 1  2    3    4    5    6    7    8