Combinations: all problems

If you have Alice, Betty, Chase, and Dave and you need to choose two of them to be the leaders of the math club, how many ways are there to do this?

Evaluate $\dbinom{8}{4}$ and $\dbinom{9}{7}$

How many ways are there to select 3 fruits amongst 8 different fruits?

How many ways are there to choose 4 balls from a bag which contains 9 balls of different color?

Mrs. Jones is organizing a potluck and wants to serve 8 different dishes. Each family can bring 3 dishes. How many families can Mrs. Jones invite so that no two families bring the same combination of dishes?

There are 9 different flavors of ice cream at an ice cream shop. Joe wants to buy 2 or 3 scoops of different ice cream flavors. He doesn't like 2 of the flavors Mango and Chocolate together so won't buy them together. How many ways can he buy ice cream?

A set of 25 square blocks is arranged into a $5 \times 5$ square. How many different combinations of 3 blocks can be selected from that set so that no two are in the same row or column?

Henry's Hamburger Haven offers its hamburgers with the following condiments: ketchup, mustard, mayonnaise, tomato, lettuce, pickles, cheese, and onions. A customer can choose one, two, or three meat patties and any collection of condiments. How many different kinds of hamburgers can be ordered?

How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.)

How many 5 digit positive integers exist such that the third digit is 8, the first 3 digits ascending, and last 3 digits are descending?

There are 12 astronauts who applied to go on a mission to explore Mars. 2 different rockets will be sent from Earth: one carrying 3 people and another carrying 4. Out of the 12 astronauts, 4 of them are very experienced so they must go on either rocket. How many ways are there to place the astronauts in the rockets?