QQuestionMathematics
QuestionMathematics
"If a person can select 3 presents from 10 presents under the tree, how many different combinations are there?
A. 120
B. 30
C. 720
D. 10"
12 months agoReport content
Answer
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Step 1:Let's solve this step by step using combination principles:
Step 2:: Identify the Problem Type
This is a combination problem where we need to calculate how many ways we can select 3 presents from a total of 10 presents.
Step 3:: Recall the Combination Formula
- $$r$$ is the number of items being selected (3 presents)
Where:
Step 4:: Calculate the Combination
\binom{10}{3} = \frac{10!}{3!(10-3)!} = \frac{10!}{3!(7)!}
Step 5:: Expand the Calculation
= \frac{10 \cdot 9 \cdot 8 \cdot 7!}{(3 \cdot 2 \cdot 1) \cdot 7!}
Step 6:: Simplify
= \frac{10 \cdot 9 \cdot 8}{3 \cdot 2 \cdot 1} = \frac{720}{6} = 120
Final Answer
Key Insight: This means there are 120 unique ways to select 3 presents from 10 presents, where the order of selection doesn't matter.
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