Discrete Math and Dividers

T

thechampion116

New member
Joined
Dec 10, 2005
Messages
9
I dont understand how to use dividers for this problem. (dividers are a must)

Question: How many numbers between 1 to 9999 have 8 as the sum of their digits.

Thanks in advance
 
Do you really mean “8 as the sum of their digits.”?
Could you mean 9 as the sum of their digits?
To use divisibility rules this makes more sense.

I can solve it with the 8 but not using divisibility rules.
Must you use the divisibility rules??
 
I mean '8' as the sum of the digits, ex 26 is 2+6=8
Yes, it needs to be done with dividers.

How would you do it without dividers, I did it by hand and came up the answer, but my teacher doesnt want it done that way. ( i need to know how to do these questions because similar ones will show up on the test)
 
You have written dividers do you mean divisors?
If not, what are dividers?
 
Let me give you the example in the book.

There are 6 people: A,B,C,D,E,F and there are 10 loonies. How many ways are there to distribute the loonies between all 6 people?

The book then lists L- loonie |-divider
L|| L| L |L L L L|| L L L (10 loonies and 5 dividers)

The loonies can be distributed in any way and 5 dividers are used because there are six people. therefore the answer is 15!(total)/(10! x 5!) = 3003
 
Well then this is usually called multi-selections.
Putting k identical items into n different cells
The number of ways to do that is Combin(k+n−1,k).

So the four digit numbers look like \(\displaystyle \L
d_4 d_3 d_2 d_1 = d_4 \cdot 1000 + d_3 \cdot 100 + d_2 \cdot 10 + d_1\).

We want the four digit to \(\displaystyle \L
d_4 + d_3 + d_2 + d_1 = 8\).

This is like putting 8 identical ones into 4 different cells.


selections1oi.gif
 
YES THAT IS CORRECT!
The number 8 is 0008. The number 26 is 0026.
The number 125 is 0125. The number 1232 is itself.
Do it all at once: Combin(8+4−1,8).
 
You must log in or register to reply here.
Top