Arun Sharma Solutions for Exercise 1: Level of Difficulty

There are $25$ points on a plane of which $7$ are collinear. Find how many quadrilaterals can be formed from these points?

A class prefect goes to meet the principal every week. His class has 30 people apart from him. If he has to take groups Of three every time he goes to the principal,
If on the very first visit the principal appoints one of the boys accompanying him as the head boy of the school and lays down the condition that the class prefect has to be accompanied by the head boy every time he comes then for a maximum of how many weeks (including the first week) can the class prefect ensure that the principal sees a fresh group of three accompanying him?

How many numbers greater than $0$ and less than a million can be formed with the digits $0, 7$ and $8$?

In how many ways is it possible to choose a white square and black square on a chessboard so that the squares must not lie in the same row or same column?

Twenty-seven persons attend a party. Which one of the following statements can never be true?

There are six boxes numbered $1,2.......6$. Each box is to be filled up either with a red or a green ball in such a way that at least one box contains a green ball and the boxes containing green balls are consecutively numbered. Find the total number of ways in which this can be done.

How many numbers can be formed with odd digits $1, 3, 5, 7, 9$ without repetition?

In how many ways, five chocolates can be chosen from an unlimited number of Cadbury, Five-star and Perk chocolates?