## 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 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

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