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Zorluk: OrtaBasic Probability and Counting Methods

A high school planning committee needs to select a subcommittee of 33 people from a pool of 55 teachers and 44 students. How many different subcommittees can be formed consisting of exactly 22 teachers and 11 student?

Cevap: 40 subcommittees

Cevap

The total number of different subcommittees that can be formed is 40.
To find the number of unique subcommittees with 2 teachers and 1 student, calculate the combination for choosing 2 teachers from 5, which equals 10, and 1 student from 4, which equals 4. Multiplying these independent choices together results in 40 possible subcommittees.

Adım Adım Çözüm

1
Calculate the number of ways to select 2 teachers from the pool of 5 teachers.
(52)=5×42×1=10\binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 ways
Selection order does not matter for committee members, so combinations are used.
2
Calculate the number of ways to select 1 student from the pool of 4 students.
(41)=4\binom{4}{1} = 4 ways
Choosing 1 item from a set of 4 offers 4 distinct possibilities.
3
Apply the Fundamental Counting Principle to determine total combinations.
10×4=4010 \times 4 = 40 subcommittees
Multiply the number of choices for teachers by the number of choices for students.

Anahtar Kavram

Combinations and Fundamental Counting Principle
Tahmini Süre:1m 0s
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Konular

Basic Probability and Counting Methods

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