word problem

• Jan 10th 2009, 06:46 PM
math123456
word problem
A number is called a decreasing number if each digit is less than the preceding digit. How many three- digit decreasing numbers are less than 500.
• Jan 10th 2009, 06:48 PM
skeeter
Quote:

Originally Posted by math123456
A number is called a decreasing number if each digit is less than the preceding digit. How many three- digit decreasing numbers are less than 500.

what does this have to do with composite functions?
• Jan 10th 2009, 06:54 PM
Jhevon
Quote:

Originally Posted by skeeter
what does this have to do with composite functions?

haha, nothing. just a case of recycling topics it seems

Quote:

Originally Posted by math123456
A number is called a decreasing number if each digit is less than the preceding digit. How many three- digit decreasing numbers are less than 500.

i suppose we are not considering numbers that begin with zero or two zeros

then you have 4 cases:

case 1: the number starts with 4

case 2: the number starts with 3

case 3: the number starts with 2

case 4: the number starts with 1

now, how many decreasing numbers are there in each case?

example: let me do the last one for you (:D)

if the first is 1, the the second digit has no choice but to be zero. but then the third digit would have to be negative. since we have to be less than the preceding digit (as opposed to less than or equal to the preceding digit) there are no decreasing numbers in this case.