# Combinations and Permutations

Combinations and permutations are fundamental concepts in combinatorics, the branch of mathematics concerned with counting and arranging objects. These concepts play a crucial role in various fields such as probability, statistics, and computer science. Combinations refer to the selection of items without considering the order, while permutations involve arranging items in a specific order. Understanding the principles of combinations and permutations is essential for solving problems involving arrangements, selections, and probability calculations. In this introductory paragraph, we will explore the basic definitions and applications of combinations and permutations, laying the foundation for further discussion.

- How many four-digit even numbers can be formed using the digits 3,4,7,8 if digits may be repeated?
- Is selecting the batting order in a baseball game a permutation or combination?
- There are 12 face cards in a standard deck of 52 cards. How many ways can you arrange a standard deck of 52 cards such that the first card is a face card?
- What are the number of different words beginning and ending with a consonant, which can made out of the word "EQUATION" ? (Using the concept of Permutations-Combinations)
- How many different student body governments are possible if there are 4 seniors, 5 juniors, and 3 sophomores running for the student body offices of senior class president, junior class president, and sophomore class president?
- How many ways can 4 students be arranged in a row?
- If you roll five dice, what are the odds of rolling five 5's?
- A red container contains 7 items of which 2 are new and 5 are old items. A purple container contains 4 items of which 1 is new and 3 are old items. An item is drawn at random from each box. 1. What is the probability that both items are old items?
- How do you evaluate 10c3?
- How many different permutations can you get from the letters in the word INVISIBILITY?
- In how many different ways can you arrange the letters of the word COMPUTER taking 4 at a time?
- A coin is tossed 20 times. What is the probability there are 17 tails?
- In a fish tank, there are 24 goldfish, 2 angel fish, and 5 guppies. If a fish is selected at random, what is the probability that it is a goldfish or an angel fish?
- How many 8-character passwords can be created from 26 lowercase letters and 10 digits, assuming that in every password there must be as many letters and numbers as?
- In how many ways can you arrange 5 books in a bookshelf?
- S With a short time remaining in the day, a FedEx driver has time to make deliveries at 6 locations among the 9 locations remaining. How many different routes are possible?
- There are 9 students in a club. Three students are to be chosen to be on the entertainment committee. In how many ways can this group be chosen?
- There are 11 qualified applicants for 7 trainee positions in a fast-food management program. How many different groups of trainees can be selected?
- A smoothie shop offers drinks with 5 types of whole fruit, 4 types of juice, and 3 flavors or yogurt. How many smoothie combinations are possible?
- What are the possible outcomes when the coin tossed 20 times?