probability We randomly choose three vertices from an octagonal pyramid.?

P(at least two chosen vertices lie on the same edge )
= 1 - P(3 chosen vertices have no any 2 lie on the same edge)
= 1 - P(3 chosen vertices at the base) * P(Such 3 vertices at the base have no any 2 lie on the same edge)
= 1 - P(3 chosen vertices at the base) * P(a such vertices at the base is not near other 2's) * (1 - P(other 2's
lie on the same edge))
= 1 - C(8,3)/C(9,3) * C(5,2)/C(7,2) * (1 - 4/C(5,2))
= 1 - 56/84 * 10/21 * (1 - 4/10)
= 1 - 2/3 * 2/7
= 17/21 = a/b
The value of a + b = 17 + 21 = 38.