Question

How many solutions (using only nonnegative integers) are there to the following equation?

x1 + x2 + x3 + x4 + x5 = 33

Answer 1

Is this for a Discrete Mathematics course?

Answer 2

Yes

Answer 3

Either that or a Brilliant.org early level problem

Answer 4

well, start with 33 + 0 + 0 + 0 + 0

then 32 + 1 + 0 + 0 + 0

so on, and so forth

Answer 5

You treat the variables as holes and the 33 as balls. So you want to find the number of ways to distribute 33 balls in 5 holes.

Answer 6

@vknight33 how many ways can you partition 33 into 5 nonnegative integers?

Answer 7

6 with 3 left over......... This course drives me insane.

Answer 8

I am going to be honest this has to be broken down like your teaching a virgin.... SMH.... I don't understand this at all

Answer 9

I can't remember the formulas right now for the problem and it would be a bit hard for me to work them out right now, as it is 4am in my country. I think that you don't care for order here, though (all balls are the same and you don't care for order in the holes).

Answer 10

@mathslover Could you help please? Thank you.

Answer 11

you want the number of combinations. i assume the x-values can repeat, here

think of it the way i had it written before.

33 + 0 + 0 + 0 + 0
32 + 1 + 0 + 0 + 0
31 + 1 + 1 + 0 + 0
30 + 1 + 1 + 1 + 0
29 + 1 + 1 + 1 + 1

so on, and so forth, until every combination of numbers is used

Answer 12

Did you understand the balls-holes similarity @vknight33 ?

Answer 13

To be honest No.... I am completely lost with this

Answer 14

re-word the question:

If i told you I had 5 numbers that add up to 33, and you needed to find these numbers, what would you do?

Answer 15

figure out the 5 numbers that total 33...

Answer 16

exactly, but, there are many ways to do that, right?

for instance, 29 + 4 + 0 + 0 + 0 are 5 numbers that add up to 33, right?

you can write this many, many different ways

Answer 17

so, in order to find the numbers I had, you would have to list every combination of numbers that adds to 33

Answer 18

which is precisely what the question is asking: how many different ways can you write 5 numbers that add up to 33?