Probability, Permutation and Combination

A coin is thrown 3 times in the air. What is the probability that one head is followed by two tails?

What is the probability of rolling an even number on a standard six-sided die?

In a box, there are 10 apples and 2/5th of the apples are rotten. If three apples are taken out from the box, what will be the probability that at least one apple is rotten.

If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much % should he reduce the quantity of gasoline that he buys?

What is the probability that an integer selected at random from those between 20 and 100 inclusive is a multiple of 15?

Committee X has 4 members, Committee Y has 5 members, and these committee's have no members in common. If a task force is to be formed consisting of one member of X and one member of Y, how many different task forces are possible

In a railway compartment 6 seats are vacant on a bench. In how many ways can 3 passengers sit on them?

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

There are 3 green, 4 orange and 5 white colour bulbs in a bag. If a bulb is picked at random, what is the probability of having either a green or a white bulb?

How many permutations of seven different letters may be made?

A committee has 5 men and 6 women. What is the number of ways of selecting a group of eight persons?

In your bookshelf, you have five favorite books. If you decide to arrange these five books in every possible combination and moved just one book in every half a minute. How much time it will take you to arrange?

In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?

In how many different ways can the letters of the word "JASHORE" be arranged so that the vowels always come together?

In a club, 60% members are male and 70% members are graduates. Also 50% of the graduate members are male. What percentage of the club members are female and non-graduate?

If two fair coins are flipped, what is the probability that one will come up heads and the other tails?

In a party 15 people shake their hands with each other. How many times did the hand-shakes take place?

All possible three digit numbers are formed by 1, 2, 3. If one number is chosen randomly; the probability that it would be divisible by 111 is -

In how many different orders can 8 different colors of flowers be arranged in a straight line?

If two coins are tossed, what is the probability of getting at least one head?