Mathematics - Permutation & Combination Question with Solution | TestHub
Using the vertices of a convex decagon, match the counts of polygons having the specified number of sides in common with the decagon. Column I: (A) Triangles with exactly one common side (B) Triangles with exactly two common sides (C) Quadrilaterals with exactly two common sides (D) Quadrilaterals with exactly three common sides Column II: (p) 75 (q) 110 (r) 60 (s) 10
Column I | Column II |
|---|---|
(A) Triangles with exactly one common side | (p) 75 |
(B) Triangles with exactly two common sides | (q) 110 |
(C) Quadrilaterals with exactly two common sides | (r) 60 |
(D) Quadrilaterals with exactly three common sides | (s) 10 |
Options:
Answer:
Solution:
For A, choose the boundary edge (10 ways), then one of six vertices not adjacent to it, giving 60. Consecutive triples give . For C, either choose two disjoint boundary edges, or a run of three consecutive vertices and a fourth nonadjacent one; together these give 75. Runs of four consecutive vertices give .
Note: the source left this key blank; mapping verified independently.
