Multiple Choice
Emily is organizing her closet. She has 15 shirts left to hang but has space in one section for 6 shirts. How many ways could she hang shirts in that section?
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10. Combinatorics & Probability
Combinatorics
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From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?
A
491,400
B
24
C
11,793,600
D
20,475
Verified step by step guidance1
Identify that this is a combination problem, where order does not matter. We need to select 4 students from a total of 28.
Use the combination formula: \( C(n, r) = \frac{n!}{r!(n-r)!} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.
Substitute the values into the formula: \( C(28, 4) = \frac{28!}{4!(28-4)!} \).
Calculate \( 28! \), \( 4! \), and \( 24! \) separately. Remember that \( n! \) (n factorial) is the product of all positive integers up to \( n \).
Divide \( 28! \) by the product of \( 4! \) and \( 24! \) to find the number of combinations, which will give you the number of ways to select 4 students from 28.
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