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Problem
How many integral Solutions are there to the system of equations
x
1
+
x
2
+
x
3
+
x
4
+
x
5
=
20
x_1+x_2+x_3+x_4+x_5=20
x
1
+
x
2
+
x
3
+
x
4
+
x
5
=
20
and
x
1
+
x
2
=
15
x_1+x_2=15
x
1
+
x
2
=
15
, when
x
i
≥
0
x_i \ge 0
x
i
≥
0
?
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