A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is:

Two cards are drawn  together from a pack of 52 cards .The probability that one is a spade and one is a heart ,is

In a simultaneous throw of two coins he probability of getting at least one head is

How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?

A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.

There are three cities A, B and C. Each of these cities is connected with the other two cities by at least one direct road. If a traveller wants to go from on city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly, there are 23 routes from B to C (including those via A). How many roads are there from A to C directly?

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

In how many distinguishably different ways can a cube be painted using at most two colours - White and Black - such that each face is coloured with exactly one of the two given colours?

Two different teams with four students each were training for an international math contest. The students were given an assessment exam and their scores were ranked. What is the probability that the four best scores come from only one of the teams assuming that no two students got the same score?