openfreebooks-bookgenerator/content/math/permutations-combinations-probability/supplement.html

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<div class="book-prose">
<h2 id="checkpoints" class="book-prose__heading">Checkpoints</h2>
<details class="book-question">
<summary class="book-question__prompt">Compute \({}_7P_3\).</summary>
<div class="book-question__solution">
<p><strong>Answer:</strong> \(7\times6\times5=210\).</p>
</div>
</details>
<details class="book-question">
<summary class="book-question__prompt">Compute \({}_8C_2\).</summary>
<div class="book-question__solution">
<p><strong>Answer:</strong> \(\frac{8\cdot7}{2}=28\).</p>
</div>
</details>
<details class="book-question">
<summary class="book-question__prompt">How many 3-letter arrangements from A,B,C,D (no repeats)?</summary>
<div class="book-question__solution">
<p><strong>Answer:</strong> \({}_4P_3=24\).</p>
</div>
</details>
<details class="book-question">
<summary class="book-question__prompt">How many ways to choose 3 students from 10?</summary>
<div class="book-question__solution">
<p><strong>Answer:</strong> \({}_{10}C_3=120\).</p>
</div>
</details>
<details class="book-question">
<summary class="book-question__prompt">A 5-card hand from 52 cards: probability all hearts.</summary>
<div class="book-question__solution">
<p><strong>Answer:</strong> \(\frac{{}_{13}C_5}{{}_{52}C_5}\).</p>
</div>
</details>
</div>