QuestionJuly 16, 2025

Students in a physics class are required to complete at least three out of a collection of nine lab projects. In how many ways can a student satisfy the requirement? A student can satisfy the requirement in square different ways

Students in a physics class are required to complete at least three out of a collection of nine lab projects. In how many ways can a student satisfy the requirement? A student can satisfy the requirement in square different ways
Students in a physics class are required to complete at least three out of a collection of nine lab projects. In how
many ways can a student satisfy the requirement?
A student can satisfy the requirement in square  different ways

Solution
3.5(281 votes)

Answer

502 Explanation 1. Determine the number of projects to choose A student must choose at least 3 projects from a total of 9. 2. Calculate combinations for choosing 3, 4, ..., 9 projects Use the combination formula: **C(n, k) = \frac{n!}{k!(n-k)!}**. Calculate C(9, 3), C(9, 4), ..., C(9, 9). 3. Sum the combinations Add the results from Step 2: C(9, 3) + C(9, 4) + \ldots + C(9, 9).

Explanation

1. Determine the number of projects to choose<br /> A student must choose at least 3 projects from a total of 9.<br />2. Calculate combinations for choosing 3, 4, ..., 9 projects<br /> Use the combination formula: **$C(n, k) = \frac{n!}{k!(n-k)!}$**. Calculate $C(9, 3)$, $C(9, 4)$, ..., $C(9, 9)$.<br />3. Sum the combinations<br /> Add the results from Step 2: $C(9, 3) + C(9, 4) + \ldots + C(9, 9)$.
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