The University of Illinois has about 40,000 students. What is the minimum number of students needed to be certain that at least two students have the same 3 initials?

Twelve people toast each other at Thanksgiving dinner. If each person clinks a glass with every other person exactly once, how many clinks are there?

How many 4 digit numbers contain no 5's? The leading digit cannot be zero.

How many different "words" can be formed using all the letters of the word IMPARTIALITY?

How many permutations are possible if six people are seated around a square table?

Four couples go to the school's drama production and sit together in a row of 8 seats. In how many ways can these people arrange themselves if each couple sits together?

Seventy-five people buy a raffle ticket for a cake drawing with four cakes. If four tickets are to be drawn, how many ways are there to award the cakes if the four cakes are identical?

There are seven seats in each row of a classroom. Luke and Lester are assigned to after-school detention and they must sit in the front row of the classroom, but they cannot sit next to each other because they might talk. How many ways can these two students be seated in the row?

The City Council is made up of nine representatives and one Chairman. If a committee of four is formed from the members, find the probability that the committee includes the Chairperson.

Four cards are dealt from a well-shuffled deck of cards. Find the probability that all four cards are Hearts.

In a survey, 60% of the students have a dog, 55% have a cat, and 32% have both a cat and dog. What is the probability that a student chosen at random has either a cat or a dog?

In a survey, 60% of the students have a dog, 55% have a cat, and 32% have both a cat and dog. What is the probability that a student chosen at random has neither a cat nor a dog?

In a discrete math class, five-eighths of the students are women. In addition, one-fifth of the women have blue eyes. Of the men, one-sixth have blue eyes. If a student is chosen at random from the class, find the probability that the student does not have blue eyes.

In a discrete math class, five-eighths of the students are women. In addition, one-fifth of the women have blue eyes. Of the men, one-sixth have blue eyes. If a person is chosen that does not have blue eyes, find the probability that the person is male.

Katie's free-throw average is 60%. What is the probability that she will successfully make exactly three of her next five free-throw attempts?

Six out of ten card players like to play bridge. If John, Jim, Graham and Vickie are card players and they are asked if the like to play bridge, what is the probability that at least three like to play bridge?

Six out of ten card players like to play bridge. If John, Jim, Graham and Vickie are card players and they are asked if the like to play bridge, what is the probability that none would like to play bridge?