SOLUTION: How many four-digit numbers can be formed under each condition? (a) The leading digit cannot be 0 and the number must be less than 2000. (b) The leading digit cannot be 0 a

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Question 1178908: How many four-digit numbers can be formed under each condition?
(a) The leading digit cannot be 0 and the number must be less than 2000.

(b) The leading digit cannot be 0 and the number must be odd.
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


a. There are two ways to select the first digit, 1 or 2, and 10 ways to select each of the next three digits, hence:



You can do your own arithmetic.


John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

(a)  The solution is VERY SIMPLE.


     Under given condition, the numbers are  integers from  1000  to  1999, inclusive.


     In all, there are exactly 1000  (one thousand) of such numbers.



(b)  As the problem is posed, it is unclear to me, what restrictions work in this case.


    If you mean odd integer numbers of the category (a), then their amount is half of the 1000 numbers of the category (a), i.e. 500.


    If you mean all odd four-digit numbers, then the amount of such numbers is  9000%2F2 = 4500.

Solved and answered.