What’s the difference between permutations and combinations?

Answer 1

combinations order doesn't matter

permutations: order matters

nCr = n!/r!(n-r)!

nPr = n!/(n-r)

for example, 3 books arranged by 2 books selected from the 3 on a shelf

have ABC books which could be AB, AC, BC 3 ways

but if order matters, the AB, AC, BC, BA, CA, CB 6 ways

3C2 = 3!/1!2! = 6/2 =3 ways

3P2 = 3!/1! = 6/1 = 6 ways

nPr = r!nCr

Answer 2

Permutations are used when order matters, and combinations are used when order doesn’t matter.

For example, choosing 3 people from a group of 5:

1. Combinations: Just the group (ABC is the same as CAB).
2. Permutations: The arrangement (ABC ≠ CAB).
3. Think of combinations as picking a team, and permutations as picking winners (1st, 2nd, 3rd).