Probability, Permutation and Combination

12 marbles are selected at random from a large collection of white, red, green and yellow marbles. The number of marbles of each color is unlimited. Find the probability that the selection contains at least one marble of each color?

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 a simultaneous throw of two dice what is the probability of getting a doublet?

Out of 10 persons working on a project, 4 are graduated. If 3 are selected, what is the probability that there is at least one graduate among them?

Three dice are thrown together. Find the probability of getting a total of at least 6?

A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?

A word consists of 9 letters; 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability that more than one vowel will be selected?

There is a group of 5 men, 6 women and 8 children. 1 man, 1 woman and one child are going to be selected to play a game. In how many ways can the selection be done?

In a simultaneous throw of a pair of dice, what is the probability of getting a total more than 8?

A coin is tossed four times. What is the probability of getting head on all tosses?

A certain jar contains 60 jellybeans 22 white, 18 green, 11 yellow, 5 red and 4 purple. If a jellybeans is to be chosen at random, what is the probability that the jellybean will be neither red nor purple ?

There are 5 red and 3 black balls in a bag. Probability of drawing a black ball is -

One-fourth of the boys and three-eight of the girls in a school participated in the annual ports. What proportional part of the total student population of the school participated in the annual sports?

ⁿC₁ + ⁿC₂ + ⁿC₃ + .. .. ⁿC_n = ?

Two dice are thrown simultaneously. What is the probability of getting the sum of the face number is odd?

There are 3 doors to a lecture room. In how many ways can a lecturer enter the room from one door and leave from another door?

In how many ways can 5 people from a group of 6 people be seated around a circle table?

Jennifer flipped a coin three times and got heads each time. What is the probability that she gets heads on the next flip?

In a certain office, the human resources department reports that 60% of the employees in the office commute over an hour on average each day, and that and that 25% of those employees, who commute over an hour on average each day commute by train. If an employee at the office is selected at random, what is the probability that the employee commutes over an hour on average by train?

There are 15 balls in a box : 8 balls are green, 4 are blue and 3 are white, Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?