What is the difference between combinations and permutations?

What is the difference between combinations and permutations?

Combinations refer to selections where the order does not matter, while permutations involve arrangements where order is important.

Can you give me an example of combinations?

Sure! If you have three fruits: an apple, a banana, and a cherry, the combinations of two fruits would be: (apple, banana), (apple, cherry), and (banana, cherry).

What about permutations? Can you show me?

Absolutely! Using the same fruits, the permutations of two fruits would be: (apple, banana), (banana, apple), (apple, cherry), (cherry, apple), (banana, cherry), and (cherry, banana).

How do I calculate combinations and permutations mathematically?

For combinations, use the formula C(n, r) = n! / (r!(n-r)!), and for permutations, use P(n, r) = n! / (n-r)!.