Chapter 13, Problem 11PT

To determine

If 15 people entered for a chance to win 3 tickets then find the probability that Jodi, Dan and Pillar all won the tickets.

Answer to Problem 11PT

The probability that each one of them will win is $\frac{1}{455}$ .

Explanation of Solution

Given information: it is given that 15 people entered to win 3 tickets.

Calculation: As the order does not matter in selection of 3 among 15 people, so it is the case of combination. Therefore the total number of outcomes will be $\left(C{}_3\right)$ and it is evaluated as,

  $\begin{array}{c}C{}_3=\frac{15!}{\left(15-3\right)!3!}\\ =\frac{\left(15\right)\left(14\right)\left(13\right)\left(12!\right)}{\left(12!\right)\left(3\right)\left(2\right)\left(1\right)}\\ =\frac{\left(15\right)\left(14\right)\left(13\right)}{6}\\ =455\end{array}$

Now the probability $\left(P\right)$ that Jodi, Dan and Pillar all won the tickets is $P=\frac{1}{455}$ because the possible outcome case for each of them to win is 1. Hence the probability that each one of them will win is $\frac{1}{455}$ .