Question 1

What's the difference between permutations and combinations?

Accepted Answer

Permutations count arrangements where order matters (like race positions: 1st, 2nd, 3rd are different). Combinations count selections where order doesn't matter (like choosing team members: selecting A,B,C is the same as C,A,B). Permutations are always ≥ combinations for the same n and r.

Question 2

When do I use permutations vs combinations?

Accepted Answer

Use permutations when order matters: arranging books on a shelf, race rankings, password sequences. Use combinations when order doesn't matter: selecting committee members, choosing pizza toppings, picking lottery numbers. Ask yourself: 'Does the order of selection change the outcome?'

Question 3

What does 'with repetition' mean?

Accepted Answer

With repetition means you can select the same item multiple times. For example, a 4-digit PIN can have repeated digits (1111 is valid). Without repetition means each item can only be selected once. Most real-world problems are without repetition unless specifically stated otherwise.

Question 4

How do I remember the formulas?

Accepted Answer

Remember: P(n,r) = n!/(n-r)! and C(n,r) = n!/(r!(n-r)!). Notice that C(n,r) = P(n,r)/r! because combinations don't care about order, so we divide out the r! ways to arrange the selected items. The combination formula has an extra r! in the denominator.

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Permutation Formula

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