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Home » But since question likely expects decimal or fraction, but format uses integers. - Blask

But since question likely expects decimal or fraction, but format uses integers. - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Solution:** To solve this problem, we use the concept of combinations, as the order in which the instruments are showcased does not matter. The number of ways to choose 4 instruments from 7 is given by the binomial coefficient \(\binom{7}{4}\). The formula for combinations is:

📌 Substituting \(n = 7\) and \(r = 4\), we get:

📌 \binom{7}{4} = \frac{7!}{4! \times (7-4)!} = \frac{7 \times 6 \times 5 \times 4!}{4! \times 3 \times 2 \times 1} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = \frac{210}{6} = 35

📌 Thus, there are \(\boxed{35}\) different sets of 4 instruments that can be chosen from the 7.

📌 Question:** An agricultural systems officer in California is planning a community program and needs to select 3 types of sustainable crops from a list of 10. In how many ways can they choose 3 crops if the order does not matter?

📌 Solution:** This is another combinations problem, where we need to choose 3 crops from a list of 10. The number of combinations is given by:

📌 \binom{10}{3} = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8 \times 7!}{3! \times 7!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = \frac{720}{6} = 120

📌 Therefore, there are \(\boxed{120}\) ways to choose 3 crops from the list of 10.

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