Chapter 8.5, Problem 1E

To determine

To fill: the blank in the given statement.

Answer to Problem 1E

“The fundamental counting principle states that if there are $m_1$ ways for one event to occur and $m_2$ ways for a second event to occur, there are $m_1\cdot m_2$ ways for both events to occur”.

Explanation of Solution

Given information:

Given statement

“The --------states that if there are $m_1$ ways for one event to occur and $m_2$ ways for a second event to occur, then there are $m_1\cdot m_2$ ways for both events to occur.

Calculation:

By the Fundamental counting principle:

Let $E_1$ and $E_2$ be two events. The first event can occur in $m_1$ different way. After $E_1$ , $E_2$ can occur in $m_2$ different ways. The number of ways these two events can occur is $m_1\cdot m_2$ Matching the above statement with the given blank sentence, we conclude that blank must be filled as follows-

“The fundamental counting principle states that if there are $m_1$ ways for one event to occur and $m_2$ ways for a second event to occur, there are $m_1\cdot m_2$ ways for both events to occur”.