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!