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Home » Let the number of neutrons be \(n\). Then: - Carbonext

Let the number of neutrons be \(n\). Then: - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Here, $ n = 12 $, $ k = 4 $, so:

📌 \binom{12 - 4 + 1}{4} = \binom{9}{4} = \frac{9 \cdot 8 \cdot 7 \cdot 6}{4 \cdot 3 \cdot 2 \cdot 1} = 126

📌 Thus, the number of valid combinations is $ \boxed{126} $.

📌 Question: In a wildlife reserve, 6 types of birds are monitored, each with a GPS device. Each device can transmit data in one of 4 frequency bands. If at least one bird must use each band, how many ways can the frequency bands be assigned to the 6 birds?

📌 Wait — that's similar to a previous problem. Let's adjust to a fresh version.

📌 Corrected question:

📌 A conservationist is deploying GPS trackers on 7 endangered birds, assigning each to one of 3 operational frequency bands. How many assignments ensure that each band is used by at least one bird?

📌 Solution: We want the number of onto functions from 7 birds to 3 bands. Using inclusion-exclusion:

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