Suppose that a class of 20 students is assigned to write an essay.       Suppose 3 essays are picked at random.       How many groups of 3 are possible?       What if the 3 essays picked at random are given awards of $20, $10, and $5.       How many groups of 3 are possible now?

At a birthday party 47 guests are in attendance and 6 of them are randomly chosen to each receive a $25 gift card. How many ways can the cards be awarded?

2. There are 6 freshmen, 7 sophomores and 5 juniors in a chess club. A group of 6 students will be chosen to complete a competition. How many combinations are possible if there is to be at least one freshman and one sophomore in the group?

Suppose there are 14 people from which you can choose a President, Vice President, and a Treasurer. How many possibilities are there?

For a Halloween party, each guest can choose from the 6 different kinds of candy to have in a prize bag. If any number of candy types can be chosen, how many candy type combinations are possible?

In a class there are 4 students who are 19 years old and obtained 80 pints in the midterm. There are 6 students who are 19 years old and obtained 50 pints in the midterm. There are 6 students who are 20 years old and obtained 80 pints in the midterm. There are n students who are 20 years old and obtained 50 pints in the midterm. There are no other students. We randomly pick a student in the class, let their age be X and their score by Y. If we are given that X, Y are independent random variables, then compute n.

In how many ways can you select a group of 7 red cards and 4 black cards from a deck containing 10 red cards and 9 black cards?

How many ways can a treasurer, vice president, and president be chosen from a group of 15 candidates?

A teacher will randomly award three students with extra credit. How many possible ways can the teacher pick these three students from a class of 20 students?

At a birthday party 34 guests are in attendance and 4 of them are randomly chosen to each receive a $25 gift card. How many ways can the cards be awarded?