00:01
In this problem, it has said that each of the 50 u .s.
00:04
States is represented in the u .s.
00:06
Senate by two senators.
00:08
Now, a committee of 15 politicians is to be chosen from among the 100 u .s.
00:13
Senators.
00:14
Now, this selection is done at random, so we need to find the probability that no two senators from the same state will be chosen.
00:21
So, the required probability will be the number of favorable outcomes divided by the total number of outcomes.
00:27
First of all, let us consider the total number of outcomes.
00:31
Now, there are a total of 100 senators, and out of them, 15 of them need to be selected in order to form the committee.
00:42
So out of 100 people, 15 can be selected in 100 c -15 ways.
00:49
And here c represents combination, and we use combination here and not permutation, because the order of selection does not matter.
00:58
Next, let us consider the number of favorable outcomes which we write in the numerator.
01:02
So we need to select the 15 politicians so that no two senators from the same state will be chosen.
01:09
So basically, this is like first of all selecting 15 states and then selecting any one senator from each of them...