There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is ________.
Answer (integer)
5626
Solution
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<col style="width: 139px">
<col style="width: 307px">
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<tr>
<th class="tg-0lax">Group A</th>
<th class="tg-0lax">Group B</th>
<th class="tg-0lax">Ways</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-0lax">$4m$<br><br>$3m+1w$<br><br>$2m+2w$<br><br>$1m+3w$<br><br>$4w$<br></td>
<td class="tg-0lax">$4w$<br><br>$1m+3w$<br><br>$2m+2w$<br><br>$3m+w$<br><br>$4m$<br></td>
<td class="tg-0lax">${ }^4 C_4 \cdot{ }^4 C_4 \quad=1$<br><br>${ }^4 C_1 \cdot{ }^5 C_1 \cdot{ }^5 C_1^4 C_3 \quad=400$<br><br>${ }^4 C_2 \cdot{ }^5 C_2{ }^5 C_2{ }^4 C_2 \quad=3600$<br><br>${ }^4 C_1{ }^5 C_3{ }^5 C_3{ }^4 C_1 \quad=1600$<br><br>${ }^5 C_4{ }^5 C_4 \quad=25$<br></td>
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<p>$$\begin{aligned}
\text { Total ways } & =1+400+3600+1600+25 \\
& =5626
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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