Permutations Practice Test 1

Case I: When A is excluded.
Number of triangles = selection of (2 points from AB) (one point from AC) + selection of (one point from AB) (two points from AC)
=mC2nC1+mC1nC2 =

1

2

(m+n−2)..... (1)
Case II: When A is included.
The triangles with one vertex at A, one point from AB and one point from AC = mn are to be added in first case.
∴ Number of triangles =mn+

1

2

mn(m+n−2) =

1

2

mn(m+2)..... (2)
∴ Required ratio =

(m+n−2)

(m+n)

.