List of practice Questions

At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?

$A,B,C,D$ are four towns, any three of which are non-colinear. In how many ways can we construct three roads (each road joins a pair of towns) so that the roads do not form a triangle?

Nine squares are chosen at random on a chessboard. What is the probability that they form a square of size $3\times 3$? 

There are six boxes numbered 1, 2, 3, 4, 5, 6. Each box is to be filled up either with a white ball or a black ball in such a manner that at least one box contains a black ball and all the boxes containing black balls are consecutively numbered. The total number of ways in which this can be done equals: