Classical

Permutations and Combinations Questions - Permutation and Combinations

26:  

How many 10 digits numbers can be written by using the digits 1 and 2 ?

A.

10C1 + 9C2

B.

210

C.

10C2

D.

10!

 
 

Option: B

Explanation :


27:  

In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answers correct is

A.

11

B.

12

C.

27

D.

63

 
 

Option: D

Explanation :


28:  

The number n of ways that an organization consisting of twenty -six members can elect a president, treasurer, and secretary (assuming no person is elected to more than one position) is

A.

15600

B.

15400

C.

15200

D.

15000

 
 

Option: A

Explanation :

The president can be elected  in twenty-six different ways; following this, the treasurer can be elected in twenty five different ways since the person chosen president is not elegible to be treasurer); and following this, the secretary can be elected in twenty-four different ways. Thus, by above principle of counting, there are
n =26 x 25 x 24 =15600 different ways in which the organization can elect the officers.


29:  

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

A.

69760

B.

30240

C.

99748

D.

none of these

 
 

Option: A

Explanation :


30:  

There are (n + 1) white and (n + 1) black balls each set numbered 1 to n + 1. The number of ways in which the balls can be arranged in a row so that adjacent balls are of different colours, is

A.

(2n + 2)!

B.

(2n + 2)! X 2

C.

(n + I)! x 2

D.

2 {(n + 1)!}2

 
 

Option: D

Explanation :




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