myself and 2 friends are a part of a group of 15 jurors. If 3 people are to be chosen, what is the probability that myself and my 2 friends are the last 3 people chosen?
To calculate the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of outcomes. Since there are 15 jurors in total and we want to choose 3, we can use the combination formula. The number of combinations of 15 jurors taken 3 at a time is given by:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of jurors and r is the number of jurors being chosen.
In this case, n = 15 and r = 3, so the number of total outcomes is:
C(15, 3) = 15! / (3!(15-3)!) = 15! / (3!12!) = (15 × 14 × 13) / (3 × 2 × 1) = 455
Now, let's determine the number of favorable outcomes. Since you and your 2 friends need to be the last 3 people chosen, the number of favorable outcomes is simply 1.
Therefore, the probability that yourself and your 2 friends are the last 3 people chosen is:
P = Favorable outcomes / Total outcomes = 1/455
So, the probability is 1/455.