Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.7 - Probability - Exercise Set - Page 1119: 27


The required solution is $\frac{1}{175711536}$

Work Step by Step

Assume the probability of a player winning the jackpot is $ P\left( E \right)$. We know that is equal to, $ P\left( E \right)=\frac{\text{number of ways winning lottery}}{\text{total number of possible combinations}}$ Firstly, determine the number of ways of selecting white balls. There are 56 white balls; selection of 5 white ball can be done as given below: $\begin{align} & {}^{56}{{C}_{5}}=\frac{56!}{\left( 56-5 \right)!5!} \\ & =\frac{56!}{51!5!} \\ & =\frac{56\cdot 55\cdot 54\cdot 53\cdot 52}{5\cdot 4\cdot 3\cdot 2\cdot 1} \\ & =3819816 \end{align}$ Then, determine the number of ways of selecting golden balls. As there are 46 balls, selection of 1 golden ball can be done as: $\begin{align} & {}^{46}{{C}_{1}}=\frac{46!}{\left( 46-1 \right)!1!} \\ & =\frac{46!}{45!1!} \\ & =\frac{46\cdot 45!}{45!} \\ & =46 \end{align}$ Thus, the total number of possible combinations of balls is: $^{46}{{C}_{1}}{{\cdot }^{56}}{{C}_{5}}=175711536$ Hence, $\frac{1}{175711536}$
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