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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

The seventh-grade students at Charleston Middle School are choosing one girl and one boy for student council. Their choices for girls are Michaela (M), Candice (C), and Raven (R), and for boys, Neil (N), Barney (B), and Ted (T). The sample space for the combined selection is represented in the table. Complete the table and the sentence beneath it.

\begin{tabular}{|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ Boys } \\
\hline & & Neil & Barney & Ted \\
\hline \multirow{3}{*}{ Girls } & Michaela & [tex]$N - M$[/tex] & [tex]$B - M$[/tex] & [tex]$T - M$[/tex] \\
\hline & Candice & [tex]$N - C$[/tex] & [tex]$B - C$[/tex] & [tex]$T - C$[/tex] \\
\hline & Raven & [tex]$N - R$[/tex] & [tex]$B - R$[/tex] & [tex]$T - R$[/tex] \\
\hline
\end{tabular}

If instead of three girls and three boys, there were four girls and four boys to choose from, the new sample size would be [tex]$\square$[/tex]



Answer :

GinnyAnswer
Let's complete the table and the sentence beneath it step-by-step.

First, fill in the rest of the table by combining each girl with each boy:

\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ Boys } \\
\hline & & Neil & Barney & Ted \\
\hline \multirow{3}{}{ Girls } & Michaela & N-M & B-M & T-M \\
\hline & Candice & N-C & B-C & T-C \\
\hline & Raven & N-R & B-R & T-R \\
\hline
\end{tabular}

Now, count the number of possible combinations (sample size). Each girl can be combined with each boy, so the total number of combinations is:
- Michaela with Neil, Barney, Ted
- Candice with Neil, Barney, Ted
- Raven with Neil, Barney, Ted

That’s 3 girls times 3 boys, which gives a total of 9 combinations. Therefore, the initial sample size is 9.

Now, if the number of choices for girls and boys both increased to 4, we would calculate the new sample size similarly. Each of the 4 girls would be combined with each of the 4 boys:

- The new sample size = 4 girls 4 boys = 16 combinations.

The final answer for the sentence beneath the table:
"If instead of three girls and three boys, there were four girls and four boys to choose from, the new sample size would be 16."

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