Three unbiased coins are tossed. What is the probability of getting at most two heads?

In a game there are 70 people in which 40 are boys and 30 are girls, out of which 10 people are selected at random. One from the total group, thus selected is selected as a leader at random. What is the probability that the person, chosen as the leader is a boy?

An urn contains 6red, 5 blue and 2 green marbles. If three marbles are picked at random, what is the probability that at least one is blue?

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?