Question

reasoning
tell whether the question can be answered using permutations or combinations. explain your reasoning.
then answer the question.

1. to complete an exam, you must answer 8 questions from a list of 10 questions. in how many ways can

you complete the exam?

Explanation:

Step1: Determine permutation or combination

We need to choose 8 questions from 10, and the order of answering doesn't matter (since answering question 1 then 2 is same as 2 then 1 for completion). So we use combinations. The formula for combinations is \( C(n,r)=\frac{n!}{r!(n - r)!} \), where \( n = 10 \), \( r=8 \). Also, note that \( C(n,r)=C(n,n - r) \), so \( C(10,8)=C(10,2) \).

Step2: Calculate \( C(10,2) \)

Using the formula \( C(n,r)=\frac{n!}{r!(n - r)!} \), for \( n = 10 \), \( r = 2 \):

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Answer:

45