A P Prabhakaran Solutions for Chapter: Permutations and Combinations, Exercise 3: OBJECTIVE TYPE QUESTIONS

There are $3$ sections in a question paper, each containing $5$ questions. A candidate has to solve any $5$questions, choosing at least one question from each section. In how many ways can he make his choice?

In how many ways can a sequence of $n$ digits be formed involving $0\text{'}s$ and $1\text{'}s$ alone, so that the sequence has at least one non-zero digit.

A triangle $ABC$ is given. If $3$ points are chosen on each of the sides $AB,BC,$ and $CA,$ then the number of triangles formed by these points, is 

If ${}^n\mathrm{P}_4{=}^n{\mathrm{P}}_5$, then $n=?$

${}^n\mathrm{C}_{r-2}+2{\times }^n{\mathrm{C}}_{r-3}{+}^n{\mathrm{C}}_{r-4}=?$

The letters of the word $STINCKY$are jumbled and rearranged in all possible ways. The words thus obtained are arranged in alphabetical order. Which of the following word will have the rank $1441$? 

There are $16$ points in a plane out of which $10$ are collinear and no three of the other $6$ are collinear. Find the number of triangles that can be formed 

The number of sides of a regular polygon which has $20$ diagonals is