Math Problem Statement
There are 5 girls and 4 boys in a classroom.How many 4 member groups can be made
Question 14Answer
a.
67
b.
78
c.
126
d.
240
Solution
To solve this problem, we need to calculate the number of ways to form a 4-member group from a total of 9 students (5 girls + 4 boys).
The formula for combinations, which gives the number of ways to choose a subset of elements from a set of elements, is given by:
Here, (total students) and (group size). So, we have:
So, the correct answer is:
c. 126
Would you like more details or have any questions about this solution? Here are some additional related questions you might find useful:
- How many 3-member groups can be made from the same set of 9 students?
- What is the probability of randomly selecting a group of 4 students that includes exactly 2 girls?
- How many ways can we form a group of 4 students with at least 1 girl?
- How many different ways can we select 2 boys and 2 girls from the group?
- If we add 1 more girl to the classroom, how many 4-member groups can be made?
Tip: When calculating combinations, the order of selection doesn't matter. This distinguishes combinations from permutations, where order is important.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations and Combinations
Formulas
Combination formula: \( \binom{n}{k} = \frac{n!}{k!(n-k)!} \)
Theorems
Basic Principle of Counting
Suitable Grade Level
Grades 9-11
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