Question 386910


1) License plates must be in the form   LLLLNNN

  where L represents a letter and N represents a number, here repetition is allowed but can't use Q or 7 

so, we can use 25 letters and 9 numbers...

each letter place can be filled by any letter and each number place can be filled 

by any number so,

no. of ways = 25*25*25*25*9*9*9
  


2) digits are 2,4,6,7,8

a) for 4 digit number ABCD,  

any digit can be placed at each place 

so, total no. of ways = 5*5*5*5 = 125 


b) here repetition is not allowed 

so, total no. of ways = 5* 4 * 3* 2 = 120 
 
another method, 
  no. of ways =  5P4 = 120  (arrangement of 4 taking 5 digits)




c) here repetition is allowed to form 3 digit number i.e  XYZ

at place of X we can put only 6, 7, or 8 i.e by 3 ways..

other places can be filled by any of 5 digits..

so, no. of ways =     3*5*5  = 75 



d)
here repetition is not allowed to form 5 digit number i.e ABCDE

similar to previous problem, place A can be filled by only 3 ways..

but here 7 is only odd digit so, to form odd number 7 must be at place E.

thus place A can be filled by only 2 ways (either 6 or 8)

and now, places B, C AND D  can be filled by any digit...

 no. of ways to fill A = 2      (either 6 or 8)

 no. of ways to fill B = 3       ( 2,4,6,8 except that on A) 

 no.  of ways to fill C = 2       ( except on A and B)
 
 no.  of ways to fill D = 1     (only one will remain)
 
 no. of ways to fill E = 1    (only 7)

total no. of ways = 2*3*2*1*1 = 12

so, total no. of odd numbers more than 60,000 =  12



if you also face difficulty to understand the concept, you are welcome to contact me by mail    sudhanshu.cochin@gmail.com