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

(a) The leading digit cannot be zero.

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

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

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

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