Dell Permutation & Combination Questions

Dell Quants Permutation & Combination Quiz

Question 1
Out of 7 consonants and 4 vowels, how many words of 3 consonants 
and 2 vowels can be formed?
A
25200
B
52000
C
120
D
24400
Question 1 Explanation: 
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3*4C2) = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 120 Required number of ways = (210 x 120) = 25200.
Question 2
A committee of 5 persons is to be formed from 6 men and 4 women. 
In how many ways can this be done when at least 2 women are 
included ?
A
196
B
186
C
190
D
200
Question 2 Explanation: 
When at least 2 women are included. The committee may consist of 3 women, 2 men : It can be done in 4C3*6C2 ways or, 4 women, 1 man : It can be done in 4C4*6C1ways or, 2 women, 3 men : It can be done in 4C2*6C3 ways. Total number of ways of forming the committees = 4C2*6C3+4C3*6C2+4C4*6C1 = 6 x 20 + 4 x 15 + 1x 6 = 120 + 60 + 6 =186
Question 3
In how many different ways can the letters of the word 'LEADING' 
be arranged in such a way that the vowels always come together?
A
720
B
520
C
700
D
750
Question 3 Explanation: 
The word ‘LEADING’ has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720
Question 4
n how many different ways can the letters of the word 'OPTICAL' 
be arranged so that the vowels always come together?
A
360
B
700
C
720
D
120
Question 4 Explanation: 
The word ‘OPTICAL’ contains 7 different letters. When the vowels OIA are always together, they can be supposed to form one letter. Then, we have to arrange the letters PTCL (OIA). Now, 5 letters can be arranged in 5! = 120 ways. The vowels (OIA) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720.
Question 5
A college has 10 basketball players. A 5-member team and a captain 
will be selected out of these 10 players. How many different 
selections can be made?
A
1260
B
1400
C
1250
D
1600
Question 5 Explanation: 
A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways. Now, the captain can be selected from these 6 players in 6 ways. Therefore, total ways the selection can be made is 210×6= 1260
Question 6
How many 4-letter words with or without meaning, can be formed 
out of the letters of the word, 'LOGARITHMS', if repetition 
of letters is not allowed?
A
4050
B
3600
C
1200
D
5040
Question 6 Explanation: 
‘LOGARITHMS’ contains 10 different letters. Required number of words = Number of arrangements of 10 letters, taking 4 at a time. = 10P4 = 5040.
Question 7
12 people at a party shake hands once with everyone else in the 
room.How many handshakes took place?
A
72
B
66
C
76
D
64
Question 7 Explanation: 
There are 12 people, so this is our n value. So, 12C21 = 66
Question 8
In how many ways can a group of 5 men and 2 women be made out 
of a total of 7 men and 3 women?
A
135
B
63
C
125
D
64
Question 8 Explanation: 
Required number of ways = = (7C5*3C2) = 63
Question 9
There are 7 non-collinear points. How many triangles can be 
drawn by joining these points?
A
10
B
30
C
35
D
60
Question 9 Explanation: 
A triangle is formed by joining any three non-collinear points in pairs. There are 7 non-collinear points The number of triangles formed = 7C3 = 35
Question 10
In how many ways a committee, consisting of 5 men and 6 women 
can be formed from 8 men and 10 women?53400
A
17610
B
11760
C
45000
D
43000
Question 10 Explanation: 
Required number of ways = = (8C5*10C6) = (8C3*10C4) = 11760
There are 10 questions to complete.