What is the difference between combinations and permutations?

What is the difference between combinations and permutations?

Combinations and permutations both deal with selecting items from a group, but they differ in order. Combinations ignore order, while permutations consider it.

Can you give me an example of each?

Sure! For combinations, if you have three fruits: apple, banana, and cherry, choosing any two (like apple and banana) is a combination. For permutations, if you arrange those same fruits, the order matters (like apple-banana vs banana-apple).

How do I calculate combinations and permutations?

To calculate combinations, use the formula C(n, r) = n! / (r!(n-r)!), where n is the total items and r is the items chosen. For permutations, use P(n, r) = n! / (n-r)!, where order matters.

What are some real-life applications of these concepts?

Combinations are used in lottery selections, while permutations are used in scheduling and arranging items, like seating guests at a wedding.