Question

How many four-digit numbers can be formed under each condition?

Answer 1

Answer: a) 9000 b) 4536 c) 4000 d) 4500

Step-by-step explanation:

Total number of digits = 10

a) The leading digit cannot be zero.

i.e The first place has only 9 choices , but the rest of places has 10 choices.

Then, the number of different 4 digit number is possible :

9 x 10 x 10 x 10 = 9000

(b) The leading digit cannot be zero and no repetition of digits is allowed.

i.e The first place has only 9 choices ( 0 is excluded) , but after the first placed occupied by a digit and 0 is included  , so the choices for second place = 9

choices for third place = 8

choices for 4th place =7

Number of 4-digit number is possible =  9 x 9 x 8 x 7 = 4536

c) The leading digit cannot be zero and the number must be less than 5000.

For Leading digit  , we can take only 1,2,3,4

i.e. choices for first place is 4 , but the rest of places has 10 choices.

Number of 4-digit number is possible =   4 x 10 x 10 x 19 = 4000

d) The leading digit cannot be zero and the number must be even.

i.e The first place has only 9 choices

The last place can have 2,4,6,8,0, i.e.   last place has 5 choices

Number of 4-digit number is possible =  9 x 10 x 10 x 5 =4500