Update Probability.md

Probability.md

@@ -2,16 +2,60 @@
 
     ![](https://latex.codecogs.com/gif.latex?\binom{n}{n_{1},&space;n_{2},&space;..,&space;n_{m}}&space;=\frac{n!}{n_{1}!n_{2}!...n_{m}!})
 
-    Phân phối n người khác nhau về m nhóm khác nhau với số lượng tương ứng: n1,n2,...,nm
+    Distribute n people to m group with respectively sizes: n1,n2...,nm
 
-    Ví du: abcd => 2 nhóm mỗi nhóm 2 người
+    Example: 4 people a,b,c,d => 2 groups, each group has 2 people:
     - (ab)(cd)
     - (ac)(bd)
     - (ad)(bc)
     - (bc)(ad)
     - (bd)(ac)
     - (cd)(ab)
 
-    Kết quả: 
-    
+    Result:
+
     ![](https://latex.codecogs.com/gif.latex?\frac{4!}{2!2!}=6)
+
+* Number of vector (x1,x2..,xm) that:
+    - ![](https://latex.codecogs.com/gif.latex?x_{i}&space;>=0)
+    - ![](https://latex.codecogs.com/gif.latex?x_{1}+x_{2}+...+x_{m}=n)
+
+    is:
+
+    ![](https://latex.codecogs.com/gif.latex?\binom{n+m-1}{m-1})
+
+    If ![](https://latex.codecogs.com/gif.latex?x_{i}&space;>=1):
+
+    ![](https://latex.codecogs.com/gif.latex?\binom{n-1}{m-1})
+
+    Example: If 8 identical blackboards are to be divided among
+4 schools, how many divisions are possible?:
+
+    x1+x2+x3+x4=8
+
+    ![](https://latex.codecogs.com/gif.latex?=\binom{8+4-1}{4-1})
+
+    if each school has to receive at least 1 blackboards:
+
+    ![](https://latex.codecogs.com/gif.latex?=\binom{8-1}{4-1})
+
+* Number of vector (x1,x2..,xm) that:
+    - ![](https://latex.codecogs.com/gif.latex?x_{i}&space;>=0)
+    - ![](https://latex.codecogs.com/gif.latex?x_{1}+x_{2}+...+x_{m}=n)
+    - ![](https://latex.codecogs.com/gif.latex?x_{i}&space;>=&space;min_{i}&space;,&space;i=1..m)
+
+    ![](https://latex.codecogs.com/gif.latex?\binom{n'+m-1}{m-1})
+
+    with
+
+    ![](https://latex.codecogs.com/gif.latex?n'&space;=&space;n&space;-&space;\sum_{i=1}^{m}min_{i})
+
+* Binomial coefficient:
+
+    ![](https://latex.codecogs.com/gif.latex?\binom{n}{k}&space;=&space;\frac{n!}{(n-k)!k!})
+
+    ![](https://latex.codecogs.com/gif.latex?\binom{n}{k}&space;=&space;\binom{n-1}{k-1}&space;+&space;\binom{n-1}{k})
+
+    ![](https://latex.codecogs.com/gif.latex?(x+y)^{n}&space;=&space;\sum_{k=0}^{n}\binom{n}{k}x^{k}y^{n-k})
+
+*