QuestionAugust 26, 2025

How many different committees with 4 members can be formed from a group of 0 students (Order is not important.) This is a Select scenario, so there will be square v committees. square Combination Permutation

How many different committees with 4 members can be formed from a group of 0 students (Order is not important.) This is a Select scenario, so there will be square v committees. square Combination Permutation
How many different committees with 4 members can be formed from a group of 0 students
(Order is not important.)
This is a Select	scenario, so there will be square  v committees.
square 
Combination
Permutation

Solution
4.3(287 votes)

Answer

126 Explanation 1. Identify the Type of Problem This is a combination problem because order does not matter. 2. Use Combination Formula Use the formula for combinations: **C(n, r) = \frac{n!}{r!(n-r)!}** where n is the total number of items to choose from, and r is the number of items to choose. 3. Apply Values to Formula Here, n = 9 and r = 4. So, C(9, 4) = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!}. 4. Calculate Factorials Calculate 9! = 362880, 4! = 24, and 5! = 120. 5. Compute the Combination C(9, 4) = \frac{362880}{24 \times 120} = \frac{362880}{2880} = 126.

Explanation

1. Identify the Type of Problem<br /> This is a combination problem because order does not matter.<br /><br />2. Use Combination Formula<br /> Use the formula for combinations: **$C(n, r) = \frac{n!}{r!(n-r)!}$** where $n$ is the total number of items to choose from, and $r$ is the number of items to choose.<br /><br />3. Apply Values to Formula<br /> Here, $n = 9$ and $r = 4$. So, $C(9, 4) = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!}$.<br /><br />4. Calculate Factorials<br /> Calculate $9! = 362880$, $4! = 24$, and $5! = 120$.<br /><br />5. Compute the Combination<br /> $C(9, 4) = \frac{362880}{24 \times 120} = \frac{362880}{2880} = 126$.
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