Question

What is the order of the group of permutations \( S_3 \)?

• A. \(3\)
• B. \(6\)
• C. \(9\)
• D. \(12\)

Hint:

Order of symmetric group \(S_n = n!\)

Answer 1

The Correct Option is B

Concept: Symmetric Group
The symmetric group \( S_n \) consists of all permutations of \( n \) elements.
Step 1: Formula for order
\[ |S_n| = n! \]
Step 2: Apply for \(S_3\)
\[ |S_3| = 3! = 3 \times 2 \times 1 = 6 \]
Step 3: Interpretation
There are 6 possible ways to arrange 3 distinct elements. Conclusion: \[ |S_3| = 6 \]