00:01
Next question we are given the us senate consists of two senators from each of the 50 states.
00:09
So total number of senators is 2 times 50 and there is 100 of them.
00:16
Now, a committee of eight senators is randomly selected.
00:20
We want to find probability it contained at least one of the two senators from a certain specified state.
00:26
For example, california state, we must have at least one of the two senators in this.
00:32
Committee of eight people.
00:34
Now i'm going to take one minus probability of the complement to this and that is none of the two from this state is chosen.
00:55
Now you know that these eight senators are selected without replacement and that after they are selected they are not arranged in any particular order or assigned into any distinct positions or titles.
01:09
So the order of selection is not important.
01:14
So without replacement order not important.
01:16
We are looking at using combination.
01:20
So if you have n distinct objects and you choose r of them, it will be n factorial over r factorial times n minus r factorial.
01:28
So in this case, it will be one minus probability none of the two is from this state.
01:34
So that means we totally do not want to choose these two persons from this state.
01:39
So we're left with 98 people to choose eights.
01:46
And probability always divide by the total number of ways in this case.
01:49
To choose eight people without any restriction...