# 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
 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 210Ã—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.