If the lengths of three sides a.b.c. of triangle ABC are all integers, and a is greater than B is greater than C, and a = 7, how many triangles satisfy the condition? Please do help me think about it

a＞b＞c,a=7,
7＞b＞c
B + C > 7 (the sum of the two sides of the triangle is greater than the third side)
There are six that meet the conditions
b+c=6+2＞7
b+c=6+3＞7
b+c=6+4＞7
b+c=6+5＞7
b+c=5+3＞7
b+c=5+4＞7

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