In how many ways can 4 students be seated in a row of 6 chairs? (2021)

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Question: In how many ways can 4 students be seated in a row of 6 chairs? (2021)

Options:

Correct Answer: 720

Exam Year: 2021

Solution:

Choose 4 chairs from 6 (6C4) and arrange 4 students (4!). Total = 15 * 24 = 360.

In how many ways can 4 students be seated in a row of 6 chairs? (2021)

In how many ways can 4 students be seated in a row of 6 chairs? (2021)

Step 1: Understand that we have 6 chairs and we need to choose 4 of them for the students.
Step 2: Calculate how many ways we can choose 4 chairs from 6. This is done using the combination formula, which is written as 6C4.
Step 3: The combination formula 6C4 can be calculated as 6! / (4! * (6-4)!). This simplifies to 15.
Step 4: Now, we need to arrange the 4 students in the 4 chosen chairs. The number of ways to arrange 4 students is calculated using the factorial of 4, which is 4!.
Step 5: Calculate 4!, which equals 24.
Step 6: Finally, multiply the number of ways to choose the chairs (15) by the number of ways to arrange the students (24). This gives us 15 * 24 = 360.

Combinatorics – The problem involves selecting a subset of chairs and arranging students, which is a fundamental concept in combinatorial mathematics.
Permutations and Combinations – The solution requires understanding how to calculate combinations (selecting chairs) and permutations (arranging students).