15 lines are concurrent at a point $P$. A line $L$ is not passing through $P$ intersects all the 15 lines and forms triangles with them. Then, the number of triangles having $L$ as one of its side is

Let $N$ be the set of positive integers. The number of distinct triplets $(x, y, z)$ satisfying $x, y, z \in N, x

A question paper has 3 parts and each part contains 4 questions. The number of different ways in which a candidate can answer 8 questions choosing at least two from each part is

$a, b, c$ are three particular speakers among the 10 speakers of a meeting. The number of ways of arranging all 10 speakers on the dias in a row so that all the three speakers $a, b, c$ do not sit together is