# Permutations and Combinations Quiz Set 013

### Question 1

How many four letter words, with all the letters different, can be formed out of the letters of the word 'BIRTHPLACE'?

A

5040.

B

5050.

C

5030.

D

5060.

Soln.
Ans: a

This word has 10 different letters. The number of possibilities is 10P4 = 5040.

### Question 2

Section A of an exam has 2 questions, B has 3 questions and C has 8 questions. In how many ways can a student attempt the paper if he has to select one question from each of these sections?

A

48.

B

53.

C

46.

D

49.

Soln.
Ans: a

Clearly, it is 2 × 3 × 8 = 48.

### Question 3

From a group of 5 men and 8 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?

A

840.

B

850.

C

830.

D

860.

Soln.
Ans: a

The required count is 8C3 × 5C2 + 8C2 × 5C3 = 840.

### Question 4

How many 5 digit numbers ending in 0 can be formed with a given set of 7 distinct digits none of which is 0? Repetition of digits is not allowed.

A

840.

B

850.

C

870.

D

860.

Soln.
Ans: a

The units place is blocked by zero. The tens place has 7 options, the hundreds place also has (7 - 1) options, and so on. This is expressed as 7 × 6 × 5 × 4 × 1, which evaluates to 840.

### Question 5

In how many ways can 5 letter words be formed by using a given set of 9 consonants?

A

15120.

B

15125.

C

15118.

D

15121.

Soln.
Ans: a

The first place can get any of the 9 consonants, the second place can then get (9 - 1), and likewise. This is expressed as 9 × 8 × 7 × 6 × 5, which evaluates to 15120.