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Question
Mathematics
On the sides AB , BC , CA of a triangle ABC , 3,4,5 distinct points (excluding vertices A , B , C ) are chosen respectively. The number of triangles that can be constructed using these chosen points as vertices are
Q. On the sides
A
B
,
BC
,
C
A
of a triangle
A
BC
,
3
,
4
,
5
distinct points (excluding vertices
A
,
B
,
C
) are chosen respectively. The number of triangles that can be constructed using these chosen points as vertices are
160
94
Permutations and Combinations
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A
215
B
205
C
210
D
220
Solution:
Number of triangles formed
=
3
C
2
×
(
4
C
1
+
5
C
1
)
+
4
C
2
×
(
3
C
1
+
5
C
1
)
+
5
C
2
×
(
3
C
1
+
4
C
1
)
+
3
C
1
×
4
C
1
×
5
C
1
=
27
+
48
+
70
+
60
=
205