Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: Assam CEE 2016

How many words can be formed from the letters of the word $\mathrm{PROGRAMMING}$ such that the words neither start with $\mathrm{M}$ nor end with $\mathrm{M}$ ?

Let $A$ be a finite set containing $n$ elements. The number of injective mappings that can be defined from $A$ to $A$ is:

The number of times the digit $7$ will be written when listing the integers from $1$ to $1000$ is

The number of different ordered triples $\left(a,b,c\right),a,b,c\in \mathrm{N}$, such that these can represent the sides of a traingle with perimeter $18$, is

Let $T_n$ denote the number of traingles which can be formed using the verticles of a regular polygon of $n$ sides. If $T_{n+1}-T_n=21$, then $n$ is equal to