Math Help - Discrete math

How do i solve the following questions?



1.How many nonnegative solutions are there to the pair of equations
x1 + x2 + x3 = 6, x1 + x2 + x3 + x4 + x5 = 15?

2. There is a train station in Smalltown where there are trains going north and trains going south. If there are 3 southbound trains and 4 northbound train departures in a day, how many ways are there to leave Smalltown by train?

1)
006
015
024
033
042
051
060
105
114
123
132
141
151
204
213
222
231
242
303
312
321
330
402
411
420
501
510
600

Think thats all of them for the first equation.

So each of those works to give you 6 for the sum of the first 3 x's so now figure out how many ways to get 9 in the last 2 spots

09
18
27
36
45
54
63
72
81
90

now multiply however many you got in each of these cases. That is how many solutions all together there are.

The second question doesnt make any sense. there are 7 trains leaving, so that seems to indicate 7 ways of leaving this town. There must be something else going on that is not indicated, because as it stands i do not see the significance of this question at all

Thank you!

I need help with one more question involving discrete math:


2)A hungry spider sits at one corner of a rectangular three-dimensional grid with 4 steps in every direction. In the opposite corner there is a juicy fly that cannot move. The spider can only move along the grid lines, that is right/left, up/down and front/back. Assuming that the spider in the upper left back corner is efficient and doesn't waste time on detours, in how many ways can it reach the fly in the lower right front corner?

Originally Posted by Hayoota

Thank you!

I need help with one more question involving discrete math:


2)A hungry spider sits at one corner of a rectangular three-dimensional grid with 4 steps in every direction. In the opposite corner there is a juicy fly that cannot move. The spider can only move along the grid lines, that is right/left, up/down and front/back. Assuming that the spider in the upper left back corner is efficient and doesn't waste time on detours, in how many ways can it reach the fly in the lower right front corner?

The rules of this forum suggest that it is conventional to put new questions in a completely new thread.