How many ways can 5 students be seated in a row of 5 chairs?

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Question: How many ways can 5 students be seated in a row of 5 chairs?

Options:

Correct Answer: 120

Solution:

The number of ways to arrange 5 students in 5 chairs is 5! = 120.

How many ways can 5 students be seated in a row of 5 chairs?

How many ways can 5 students be seated in a row of 5 chairs?

Step 1: Understand that we have 5 students and 5 chairs.
Step 2: Realize that each student can sit in any of the chairs.
Step 3: For the first chair, there are 5 choices (any of the 5 students can sit there).
Step 4: After the first student sits down, there are 4 students left for the second chair.
Step 5: For the second chair, there are 4 choices (the remaining students).
Step 6: For the third chair, there are 3 students left, so there are 3 choices.
Step 7: For the fourth chair, there are 2 students left, so there are 2 choices.
Step 8: For the last chair, there is only 1 student left, so there is 1 choice.
Step 9: Multiply the number of choices together: 5 * 4 * 3 * 2 * 1.
Step 10: Calculate the result: 5 * 4 * 3 * 2 * 1 = 120.
Step 11: Conclude that there are 120 different ways to arrange the 5 students in the 5 chairs.

Permutations – The question tests the understanding of permutations, specifically how to arrange a set number of distinct items (students) in a specific order (chairs).