COMBINATION

Combination

Definition Of Combination

A combination is an arrangement of objects in which order does not matter.

Video Examples: Combinations - Counting Using Combinations

Example of Combination

There are 3 books on a shelf, a Math (M) book, a Science (S) book, and a French (F) book.
John wants to take any 2 books out.
The possibilities are: MS MF
SM SF
FM FS
Remove the repetitions SM, FM, FS as they are the same as MS, MF, and SF. Now, we are left with only 3 possibilities and they tell us the combinations of books that John can probably take out.

Solved Example onCombination

Ques: Find the number of possibilities of picking a ball from 3 balls.

Choices:

A. 1
B. 2
C. 3
D. 0
Correct Answer: C

Solution:

Step 1: The possibility of picking one ball from three balls is 3C₁ = 3.

Quick Summary

Combinations are selections where order is irrelevant.
The formula nCr calculates the number of combinations of choosing r items from n items.

\[ nCr = n! / (r! * (n-r)!) \]

🍎 Teacher Insights

Use real-world examples to illustrate combinations, such as forming a committee or selecting pizza toppings. Emphasize the distinction between combinations and permutations.

🎓 Prerequisites

Factorials
Permutations
Basic Set Theory

Check Your Knowledge

Q1: How many ways can you choose 2 books from a set of 3?

1 2 3 6

Q2: What is 5C2?

5 10 15 20

Frequently Asked Questions

Q: What is the difference between permutation and combination?
A: Permutation considers order, while combination does not.

Q: When should I use combinations instead of permutations?
A: Use combinations when the order of selection doesn't affect the outcome.