A large pile of coins consists of pennies, nickels, dimes, and quarters (at least 20 of each).
(a) How many diﬀerent collections of 20 coins can be chosen?
(b) How many diﬀerent collections of 20 coins chosen at random will contain at least 3 coins of each type?
(c) What is the probability that a collection of 20 coins chosen at random will contain at least 3 coins of each type?

Question

Quizplus · Accepted Answer

The Answer is a. By Theorem 9.6.1 (about

r

-combinations with repetition allowed), there are

\left( \begin{array} { c } 20 + 4 - 1 \ 20 \end{array} ight) =

1,771 different collections of 20 coins that can be chosen.
b. There are

\left( \begin{array} { c } 8 + 4 - 1 \ 8 \end{array} ight) = 165

different collections of 20 coins that can be chosen if there must be at least 3 coins of each type.
c. The probability that a collection of 20 coins chosen at random will contain at least 3 coins of each type is

\frac { 165 } { 1771 } \cong 9.3 \%

.

A Large Pile of Coins Consists of Pennies, Nickels, Dimes