Math Problem Statement
How many different committees can be formed from
99
teachers and
3636
students if the committee consists of
33
teachers and
44
students?
Question content area bottom
Part 1
The committee of
77
members can be selected in
different ways.
Solution
To determine how many different committees can be formed from 99 teachers and 3636 students where the committee consists of 33 teachers and 44 students, we need to use the concept of combinations.
Step-by-Step Solution:
-
Combinations Formula: The number of ways to choose objects from objects is given by the combination formula:
-
Select Teachers: We need to choose 3 teachers from 99 teachers.
-
Select Students: We need to choose 4 students from 3636 students.
-
Calculate Each Combination:
-
Total Number of Ways to Form the Committee: The total number of different committees is the product of the combinations of teachers and students.
So, the committee of 7 members (3 teachers and 4 students) can be selected in different ways.
If you have any further questions or need additional details, feel free to ask!
Suggested Questions:
- How many ways can you form a committee of 5 people from 12?
- What is the probability of selecting 2 red cards from a standard deck of cards?
- How many ways can you arrange the letters in the word "MATHEMATICS"?
- What is the probability of drawing a face card and a number card from a deck?
- How many different 3-letter combinations can be formed from the alphabet?
Tip:
When dealing with combinations, always ensure to distinguish between combination and permutation problems. Combinations are used when the order does not matter, while permutations are used when the order does matter.
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Math Problem Analysis
Mathematical Concepts
Combinations
Formulas
Combination formula C(n, r) = n! / (r!(n - r)!)
Theorems
-
Suitable Grade Level
Advanced High School
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