Please enable JavaScript.
Coggle requires JavaScript to display documents.
introduction of probability (計數技術: combination (Binomial Theorem 二項式定理,…
introduction of
probability
利用data來: 推測/ 做結論
計數技術: combination
Multiplication Rule
Theorem:
If E1 is an experiment with n1 outcomes and E2 is an experiment with n2 possible outcomes, then the experiment which consists of performing E1 first and then E2 consists of n1n2 possible outcomes.
Find the possible number of outcomes in sequence of two tosses of a fair coin.
Permutation 排列
Consider a set of 4 objects. Suppose we want to fill 3 positions with objects selected from the above 4. Then the number of possible ordered arrangements is 24
(4)(3)(2)=24
In general, if r positions are to be filled from n objects, then the total number of possible ways they can be filled are given by n(n1)(n2)···(nr+1) = n! / (n-r)! = nPr.
Thus, nPr represents the number of ways r positions can be filled from n objects.
Combination組合
In permutation, order is important. But in many problems the order of selection is not important and interest centers only on the set of r objects.
Let c denote the number of subsets of size r that can be selected from n different objects.
The number c is denoted by (n r)
Example:
How many committees of two chemists and one physicist can be formed from 4 chemists and 3 physicists?
Binomial Theorem
二項式定理
Binomial series
