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A humanities course reading list has 10 books total: 4 are biographies and 6 are novels. Each student must choose 4 books, with at least 2 biographies required. How many valid 4-book selections are possible?
We need to count selections of 4 books that include 2 or more biographies (from 4 biographies and 6 novels).
Case 1 — Exactly 2 biographies + 2 novels:
$\binom{4}{2} \times \binom{6}{2} = 6 \times 15 = 90$
Case 2 — Exactly 3 biographies + 1 novel:
$\binom{4}{3} \times \binom{6}{1} = 4 \times 6 = 24$
Case 3 — Exactly 4 biographies + 0 novels:
$\binom{4}{4} \times \binom{6}{0} = 1 \times 1 = 1$
Total $= 90 + 24 + 1 = \mathbf{115}$.
From the caffeine bar graph:
- The minimum caffeine in drip-brewed coffee (5 oz) is approximately 60 mg.
- The maximum caffeine in cocoa (5 oz) is approximately 20 mg.
Difference $= 60 - 20 = \mathbf{40}$ mg.
Answer: approximately 40 milligrams.
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