📚 Considering Order – Permutations for Seats
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Question:
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Suppose 5 students are to be seated on 5 chairs. How many possibilities are there if the order matters?
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Step-by-step Solution:
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- Permutations count all arrangements when order matters: \( n! \)
- Plug in for 5 students: \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)
- This means: There are 120 different ways to seat the 5 students.
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Note: If not all seats are filled (e.g., 3 out of 5), you would calculate \( P(5,~3) = 5 \times 4 \times 3 = 60\) possibilities.
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Answer:
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With all seats occupied, there are 120 different seating arrangements.
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⚙ permutation