What is the difference between permutations and combinations

What is the difference between permutations and combinations?

When can each of them be used?

Solution

Permutation is selection of set of quantities with also giving priority to the position of the quantity.

Combination is selection of set of quantities, but the order or position of the quantity is not necessary.

For example:

If there is a race held between ten people the selection of the first, second, and the third winner is taken as permutation. While any three of the 10 are selected in combination.

Permutation: First person is selected in 10 ways. Second person can be selected in 9 ways excluding the first one and third person can be selected in 8 ways excluding the previous two people. =>10_p310x9x8=720 ways

Combination: Selecting of any 3 out of 10 =>10_c3 =(10x9x8)/(1x2x3)=120 ways