Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: BITSAT 2017

A person writes letter to six friends and addresses the corresponding envelopes. Let $x$ be the numbers of ways so that at least two of the letters are in wrong envelopes and $y$ be the numbers of ways so that all the letters are in wrong envelopes. Then $x-y=$

If a parallelogram is cut by two sets of $m$ lines parallel to its sides, then the number of parallelogram thus formed, is

The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$, is