Fundamental counting principle permutations and combinations worksheet answers – Unveiling the Fundamental Counting Principle, Permutations, and Combinations Worksheet Answers, this comprehensive guide delves into the intricacies of counting techniques, empowering you to solve complex combinatorial problems with precision and finesse.
Embark on a journey of mathematical discovery as we explore the fundamental counting principle, unlocking the secrets of counting possibilities. Delve into the world of permutations, mastering the art of arranging objects in specific orders, and unravel the mysteries of combinations, understanding the intricacies of selecting objects without regard to order.
Prepare to conquer any combinatorial challenge with this invaluable resource.
Fundamental Counting Principle: Fundamental Counting Principle Permutations And Combinations Worksheet Answers
The fundamental counting principle states that if there are n ways to do one thing and m ways to do another thing, then there are n x m ways to do both things.
For example, if there are 3 different shirts and 2 different pairs of pants, then there are 3 x 2 = 6 different ways to wear an outfit.
Permutations
A permutation is an arrangement of objects in a specific order.
The number of permutations of n objects is n!
For example, the number of permutations of the letters A, B, and C is 3! = 6.
Combinations
A combination is a selection of objects in which the order does not matter.
The number of combinations of n objects taken r at a time is nCr = n! / (r! x (n – r)!).
For example, the number of combinations of 5 objects taken 2 at a time is 5C2 = 5! / (2! x (5 – 2)!) = 10.
Worksheet Answers
| Problem | Answer | Explanation |
|---|---|---|
| How many different outfits can be made with 3 shirts and 2 pairs of pants? | 6 | There are 3 ways to choose a shirt and 2 ways to choose a pair of pants, so there are 3 x 2 = 6 different outfits. |
| How many different ways can 5 people line up in a row? | 120 | There are 5! = 120 different ways to line up 5 people in a row. |
| How many different ways can a committee of 3 people be chosen from a group of 5 people? | 10 | There are 5C3 = 10 different ways to choose a committee of 3 people from a group of 5 people. |
Common Queries
What is the fundamental counting principle?
The fundamental counting principle states that if there are n ways to do one thing and m ways to do another thing, then there are n x m ways to do both things.
How do you calculate the number of permutations of n objects?
The number of permutations of n objects is n!
How do you calculate the number of combinations of n objects taken r at a time?
The number of combinations of n objects taken r at a time is nCr = n! / (r! x (n-r)!)
