4 people are chosen at random from a group of 15 people. What are the odds that all 4 people chosen were the oldest people in the group?
To calculate the odds of all 4 people chosen being the oldest in the group, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes. Since we are choosing 4 people from a group of 15, we can use the combination formula:
nCr = n! / (r!(n - r)!)
where n is the total number of people in the group and r is the number of people we are choosing.
In this case, n = 15 (total number of people) and r = 4 (number of people chosen). So, the total number of possible outcomes is:
15C4 = 15! / (4!(15 - 4)!) = 1365
Now, let's determine the number of favorable outcomes, which is the number of ways we can choose all 4 oldest people from the group. If we assume that the oldest people in the group are known and distinct from the other people, there is only 1 way to choose all 4 of them.
Therefore, the number of favorable outcomes is 1.
Now, we can calculate the odds by dividing the number of favorable outcomes by the total number of possible outcomes:
Odds = Number of favorable outcomes / Total number of possible outcomes
Odds = 1 / 1365
So, the odds of all 4 people chosen being the oldest in the group are 1 in 1365.