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Home » Solution: Multiply $ \frac34 $ by $ \frac52 $: - Professionaloutdoormedia

Solution: Multiply $ \frac34 $ by $ \frac52 $: - Professionaloutdoormedia

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 \binom{n - k + 1}{k}

📌 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?

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