What are combinations and permutations?

Can you explain the difference between combinations and permutations?

Sure! Combinations refer to selections where the order doesn't matter, while permutations involve arrangements where order is important.

Can you give me an example of each?

Of course! For combinations, if you have 3 fruits: apple, banana, and cherry, choosing 2 fruits can be (apple, banana) or (banana, cherry). For permutations, arranging the same fruits in different orders like (apple, banana, cherry) or (cherry, apple, banana) matters.

How do I calculate combinations and permutations mathematically?

For 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)!

Can you show me a calculation example for both?

Sure! For combinations, if you want to choose 2 from 4 items: C(4, 2) = 4! / (2! * 2!) = 6. For permutations, choosing 2 from 4: P(4, 2) = 4! / (4-2)! = 12.