Prob and Stats1: Probability
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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!
