# Prob and Stats1: Probability

Permutation & Combination

Probability is based on events, which is a set of possible outcomes of a experiment. Each event is a subset of sample space. Pr(A) is the probability that A event will occur, given a experiment.

# Permutations

The number of distinct orderings of k items selected without replacement from a collection of n different items(0<k<n) is

## Arranging Books

Suppose that six different books are to be arranged on a shelf. The number of possible permutations of the book is?

## The Birthday Problem

# Combinations

Number of distinct subset of size k that can be chosen from a set of size n is

## Unordered Sampling

**Select a Committee**

**Select Baked Goods**

**Tossing a Coin**

**Playing cards**

## Ordered Sampling

**Playing cards Revisited**

## Multinomial Coefficients

Count the number of ways to partition a finite set into more than two disjointed subsets.

**Choosing Committee**

**Rolling Dice**

**Playing Cards**

## ⭐️Difference Between Permutation and Combination

In Permutation, order is a factor. In Combination, order is not a factor. Since in combination order is not a factor, many subsets are duplicate, it has fewer possibility than permutation.

**Answers for above questions can be found in Probability and Statistics by Morris H. Degroot. Thanks for reading the post. Hope it is useful!**