What is the difference between combinations and permutations?

Can you explain the difference between combinations and permutations?

Sure! Combinations refer to selecting items without regard to the order, while permutations consider the order.

Can you give me an example of each?

Of course! For combinations, if you have 3 fruits (apple, banana, cherry) and choose 2, the combinations are: (apple, banana), (apple, cherry), (banana, cherry). For permutations, if you arrange 2 fruits, the permutations are: (apple, banana), (banana, apple), (apple, cherry), (cherry, apple), etc.

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)!, where n is the total items and r is the items arranged.

What are some real-life applications of combinations and permutations?

They are used in various fields like statistics, probability, and even in game theory to determine outcomes and strategies.