Permutations Practice Test 1

Question : 4 of 40

Marks: +1, -0

The straight lines

I_1, I _2, I _3

are parallel and lie in the same plane. A total number of m points are taken on

I_1

; n points on

I_2

, k points on

I_3

. The maximum number of triangles formed with vertices at these points are:

Solution:

Total no. of points are m + n + k. The Δ’s formed by these points

= ^{m+n+k}C_3

.
Joining 3 points on the same point gives no triangle, such Δ’s are

^mC_3 + ^nC_3 + ^kC_3

.
∴ Required number

=^{ m+n+k}C_3 - ^mC_3 - ^nC_3 - ^k C_3

Go to Question:

Prev Question

Next Question