7/3 Learning essay of probability

Today I learned another nice propertof Pascal's triangle.

Choosing K people from N people equals to the number of ways of choosing k-1 people from N-1 people, plus the number of ways of choosing K people from N-1 people.

It's easy and very intuitive to understand without invoking any math.

Let's say one person of them name Alice and single her out.

Then the ways of choosing K people to be committees will have two types of doing it, with Alice or without Alice.

First, if Alice is going to be one of the K committees, then the equation will be like choosing K-1 people from N-1 people.

Second situation, without Alice to be elected as committe, then the equation is going to be like choosing K from N-1 people.

So choosing K from N people to be committees is going to equal choosing k-1 people from n-1 people, plus the number of ways of choosing k people from n-1 people.

Awesome, you learn that, Wallace Tiger, expecting tomorrow's new fresh ideas : )