Seorang murid diminta mengerjakan 5 dari 6 soal ulangan tetapi soal nomor 1 harus dipilih. Banyaknya pilihan yang dapat diambil murid tersebut adalah....

1. Break Down the Problem

• The student must choose 5 questions out of a total of 6.
• However, one specific question (question number 1) must be included in the selection.
• Consequently, the student needs to choose 4 more questions from the remaining 5 questions (questions 2 to 6).

2. Relevant Concepts

• The problem can be solved using the concept of combinations, denoted as $C(n, r)$, where $n$ is the total number of items to choose from, and $r$ is the number of items to choose.

3. Analysis and Detail

• Since question 1 is mandatory, we only need to choose 4 from the remaining 5 questions.
• The combination formula is given by:

$C(n, r) = \frac{n!}{r! \cdot (n-r)!}$

• In this case, we need to calculate $C(5, 4)$.

4. Verify and Summarize

• Calculating $C(5, 4)$:

$C(5, 4) = \frac{5!}{4! \cdot (5-4)!} = \frac{5 \times 4!}{4! \times 1!} = \frac{5}{1} = 5$

Final Answer

The number of choices the student can take is 5.