Permutations and Combinations | Probability Theory

Permutations

Permutations talk about order of things. Permutations are used in specifying lists (order matters).

Examples:

That means selecting ‘r’ things from a group of ‘n’ things in order. Note that order of things is important in permutations. So, AB and BA are different in permutations.

Combinations

Order does not matter when we talk about combination of things. Here AB and BA are same. For combinations, only final result matters, not how you get it.

Examples:

1. Fruit salad is a combination (mix) of apples, grapes and bananas
2. Picking a team of 3 people from a group of 10.

Fundamental rules of counting

Rule 1 (Fundamental rule f counting)

Suppose one operation has m possible outcomes and that a 2^nd operation has n outcomes. The number of possible outcomes when performing the first operation followed by 2^nd operation = mxn. It can be extended to 3 or more variables

Ex 1: If coin is tossed 5 times, total outcomes = 2x2x2x2x2 = 32 = 2⁵

Ex 2: If die is thrown and a coin is tossed, how many different outcomes are possible?

Die outcomes = 6 = {1,2,3,4,5,6}

Coin outcome = 2 = {H,T}

Total outcomes (rule 1) = 6×2 = 12

Sample space  = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H),), (1,T), (1,T), (1,T), (1,T), (1,T)}

Rule 2 (Fundamental rule of counting)

The number of possible outcomes of 1^st operation or 2^nd operation = m + n