SOLUTION: A number is a decreasing number if it has two or more digits and each digit is less than the digit to its left. For example 754 and 620 are decreasing numbers, but 756 and 6220 ar

Question 3491: A number is a decreasing number if it has two or more digits and each digit is less than the digit to its left. For example 754 and 620 are decreasing numbers, but 756 and 6220 are not decreasing numbers. How many decreasing numbers are there?
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
You did not mention that how many total digits in the decreasing number.
In fact,the longest possible decreasing integer is 9876543210. iT
contains 10 digits.
Now, I consider all possible cases:

(i)Ten digits: C(10,10) = 1. [There is only one number,namely 9876543210]
(ii)Nine digits: there are C(10,9) = 10 dec. numbers.
...
r digits, r>=2,: there are C(10,r) dec. numbers.
Totally, there are C(10,10)+C(10,9)+..+C(10,2) = 2^10 -C(10,1) -C(10,0)
= 1024 - 11 = 1013 such dec. numbers. (two or more digits)
Kenny
RELATED QUESTIONS
its a three digit number, its divisable by 5 it an odd number each of is digits are... (answered by edjones)

A two-digit counting number has a value that is 7 more than 6 times the sum of its... (answered by josgarithmetic)

A two digit counting number has a value that is 7 more than 6 times the sum of its... (answered by ankor@dixie-net.com)

A two digit number is two less than six timers the sum of its digits. The tens digit is... (answered by Paul)

A two-digit number is eighteen more than the sum of its digits. The tens digit is three... (answered by mananth)

Five times the sum of the digits of a two-digit number is 13 less than the original... (answered by amarjeeth123)

Five times the sum of the digits of a two-digit number is 13 less than the original... (answered by josmiceli)

Five times the sum of the digits of a two-digit number is 13 less than the original... (answered by lwsshak3)

Five times the sum of the digits of a two-digit number is 13 less than the original... (answered by MathTherapy)