Mastering Permutations and Combinations

How many different ways can the letters of the word "MATH" be arranged?

In how many ways can a committee of 3 members be selected from a group of 10 people?

What is $$5!$$

Using the counting principle, how many different two-letter codes can be created using the letters A, B, C, and D without repeating letters?

What is the probability of randomly arranging the letters in the word "DEED" such that the two E's are next to each other?

From a group of 8 women and 6 men, a committee of 5 people is to be formed. How many different committees can be formed if the committee must consist of 3 women and 2 men?

If there are 4 different books on mathematics, 3 different books on physics, and 2 different books on chemistry, in how many ways can the books be arranged on a shelf if the books on the same subject must be kept together?

In how many ways can 5 different prizes be distributed among 4 students if each student can receive any number of prizes?

What is the probability of getting exactly two heads in four flips of a fair coin?

If a password is made by choosing three distinct letters from the alphabet, with letters being able to repeat, how many different passwords can be created?