Math Problem Statement
In how many different ways can the director of research laboratory choose 2 chemists from among 7 applicants and 3 physicists from among 9 applicants? (3 points)
Solution
To find how many different ways the director of a research laboratory can choose 2 chemists from among 7 applicants and 3 physicists from among 9 applicants, we can solve this using the concept of combinations.
The formula for combinations is given by:
Where:
- is the total number of applicants,
- is the number of people to choose,
- represents the number of ways to choose applicants from .
Step 1: Choosing 2 chemists from 7 applicants
The number of ways to choose 2 chemists from 7 applicants is:
Step 2: Choosing 3 physicists from 9 applicants
The number of ways to choose 3 physicists from 9 applicants is:
Step 3: Total number of ways
Since the two events (choosing chemists and choosing physicists) are independent, we multiply the two results to get the total number of ways:
Thus, the director can choose 2 chemists and 3 physicists in 1,764 different ways.
Do you want more details or have any other questions?
Here are 5 questions to further expand on this:
- How would the result change if the director had to choose 3 chemists instead of 2?
- What is the total number of ways to choose at least 1 chemist and 1 physicist?
- Can combinations be used for selecting people when order matters?
- What is the difference between combinations and permutations?
- How does the formula for combinations change if there are identical applicants?
Tip: When dealing with combinations, order does not matter, unlike in permutations.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Combinations
Formulas
C(n, r) = n! / (r!(n - r)!)
Theorems
Combination theorem
Suitable Grade Level
Grades 10-12
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