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Banyaknya cara pemilihan wakil kelas terdiri 3 anak untuk mengikuti rapat OSIS dari kelas yang mempunyai anggota 35 anak adalah...

Mathematics

ScanSolve AI Answer

Step-by-step solution

4 steps

This problem asks for the number of ways to choose 3 students from a group of 35 students. Since the order in which the students are chosen does not matter, this is a combination problem.

  1. Identify the combination formula.

    The number of combinations of choosing kk items from a set of nn items is given by the formula:

    C(n,k)=(nk)=n!k!(n−k)!C(n, k) = \binom{n}{k} = \frac{n!}{k!(n-k)!}

    Here, n=35n = 35 (total number of students) and k=3k = 3 (number of students to be chosen).

  2. Substitute the values into the formula.

    C(35,3)=35!3!(35−3)!C(35, 3) = \frac{35!}{3!(35-3)!} C(35,3)=35!3!32!C(35, 3) = \frac{35!}{3!32!}
  3. Expand the factorials and simplify.

    C(35,3)=35×34×33×32!(3×2×1)×32!C(35, 3) = \frac{35 \times 34 \times 33 \times 32!}{ (3 \times 2 \times 1) \times 32!}

    Cancel out 32!32! from the numerator and denominator:

    C(35,3)=35×34×333×2×1C(35, 3) = \frac{35 \times 34 \times 33}{3 \times 2 \times 1} C(35,3)=35×34×336C(35, 3) = \frac{35 \times 34 \times 33}{6}
  4. Perform the multiplication and division.

    C(35,3)=35×342×333C(35, 3) = 35 \times \frac{34}{2} \times \frac{33}{3} C(35,3)=35×17×11C(35, 3) = 35 \times 17 \times 11 C(35,3)=595×11C(35, 3) = 595 \times 11 C(35,3)=6545C(35, 3) = 6545

    The number of ways to choose 3 students from 35 is 6545.

    Comparing this result with the given options:
    A. 6.545
    B. 11.456
    C. 13.090
    D. 39.270
    E. 43.089

    The calculated value matches option A.

    The final answer is A. 6.545\boxed{\text{A. 6.545}}.

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