Question

How many solutions (using only nonnegative integers) are there to the following equation?
x1 + x2 + x3 + x4 + x5 = 31

Answer 1

https://en.wikipedia.org/wiki/Combination#Number_of_combinations_with_repetition

Answer 2

You can view this question as putting 4 separators between 31 same objects.

Answer 3

I did that and got 214 which is incorrect, what am I missing?

Answer 4

how did you get 214? :)

Answer 5

I factorialed 5 then added each object

Answer 6

It should be \(((31,4))\) (or 31 multichoose 4)

Answer 7

So 744?

Answer 8

nope :/

Answer 9

wait sorry

Answer 10

how did you reach your answer then?

Answer 11

it's not \(((31,4))\)

Answer 12

it should be \(((33,4))\) since there are 33 spaces to put 4 separators.
Let me illustrate this

Answer 13

Okay

Answer 14

So its 2592