Question

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

Answer 1

Answer:

(a) 900

(b) 648

(c) 180

(d) 600

Step-by-step explanation:

If there are no restrictions, there are 10 possible values for each digit of a three-digit number.

(a) The leading digit cannot be zero

There are 9 options for the first digit and 10 for the remaining digits.

$n=9*10*10 = 900$

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

$n=9*9*8=648$

(c) The leading digit cannot be zero and the number must be a multiple of 5.

If a number is a multiple of five, it must end in 0 or 5

$n=9*10*2=180$

(d) The number is at least 400.

If the number is at least 400, the first digit can only be 4, 5, 6, 7, 8 or 9. There are no restrictions for the remaining digits.

$n=6*10*10=600$