An increasing number has its digits increase in size from left to right. For example, 24589 is an increasing number. How many four-digit increasing numbers are there? The

Guest Feb 7, 2018

#1**+2 **

An increasing number has its digits increase in size from left to right. For example, 24589 is an increasing number. How many four-digit increasing numbers are there?

There are 10C4 ways to choose 4 digits that is 210 ways

Now for each of these combiations there is exactly 1 where the digits are in ascenting order.

So that is still 210 ways.

If you discount numbers beginning with 0 then that gets harder.

Lets see... if the first one is 0 how many ways can the others be chosen. 9C3=84 ways

So I think there are 210-84= 126 ways

So there are 126 numbers that meet this criterion.

Melody
Feb 7, 2018

#2**+2 **

Here's another approach ......

1 in 1st position and then - C(8,3) - 56

2 in 1st position and then - C (7,3) - 35

3 in 1st position and then - C (6,3) - 20

4 in 1st position and then - C (5,3) - 10

5 in 1st position and then - C ( 4,3) - 4

6 in 1st position and then - C (3,3) - 1

_____

126

Just as Melody found !!!

CPhill
Feb 7, 2018