Classical

Permutations and Combinations Questions - Permutation and Combinations

31:  

In a football championship, 153 matches were played. Every team played one match with each other. The number of teams participating in the championship is

A.

17

B.

18

C.

9

D.

none of these

 
 

Option: B

Explanation :


32:  

Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?

A.

60

B.

20

C.

15

D.

125

 
 

Option: A

Explanation :


33:  

Number n of license plates that can be made where each plate contains two distinct letters followed by three different digits is

A.

486000

B.

468000

C.

498000

D.

489000

 
 

Option: B

Explanation :

n = 26 x 25 x 10 x 9 x 8 = 468000.
i.e. there are twenty-six choices for the first letter, but only twenty-five choices for the second letter which must be different from the first letter. Similarly, choices for the digits are 10, 9 and 8 since the digits must be distinct.


34:  

Six teachers and six students have to sit round a circular table such that there is a teacher between any two students. The number of ways in which they can sit is

A.

6 ! x 6 !

B.

5 ! x 6 !

C.

5! x 5!

D.

none of these

 
 

Option: D

Explanation :


35:  

The number of ways in which three girls and nine boys can be seated in two vans each having numbered seats with four in the back and three in the fron t?

A.

7!

B.

2 (7!)

C.

7 (13!)

D.

12!

 
 

Option: C

Explanation :




Suggest an improvement