Classical

Combinatories - Combinatories MCQ

21:  

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 diferent colours, is

A.

(2n+2) !

B.

(2n+2) ! x 2

C.

(n+1) ! x 2

D.

2[(n+1) ! ]2

 
 

Option: D

Explanation :


22:  

Number n of license plates that can be made where each plate contains two distinct letters followed

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.


23:  

Suppose a licence plate contains two letters followed by three digits with the first digit not zero. How many different licence plates can be pinted?

A.

608000

B.

608200

C.

608400

D.

608600

 
 

Option: C

Explanation :

Each letter can be printed in twenty-six diferent ways, the first digit in nine ways and each of the other two digits in ten ways. Hence 26 x 26 x 9 x 10 x 10 = 608400 different plates can be printed.


24:  

Common data  for next 2 questions

Given : npr = 3024.

Value of n will be

A.

3

B.

4

C.

6

D.

9

 
 

Option: D

Explanation :

Since np is product of consecutive positive integers, npr=3024=9x8x7x6
Hence n=9 and r = 4


25:  

Value of r will be

A.

3

B.

4

C.

6

D.

9

 
 

Option: B

Explanation :

Since np is product of consecutive positive integers, npr=3024=9x8x7x6
Hence n=9 and r = 4




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