Number of One-One Functions
🎥 Video Explanation
📝 Question
Set \(A\) has 7 elements and set \(B\) has 10 elements.
Find number of one-one functions from \(A\) to \(B\).
- (a) \({}^{10}C_7\)
- (b) \({}^{10}C_7 \times 7!\)
- (c) \(7^{10}\)
- (d) \(10^7\)
✅ Solution
🔹 Step 1: Formula for One-One Functions
Number of injective functions from \(n\) elements to \(m\) elements:
\[ {}^mP_n = \frac{m!}{(m-n)!} \] —
🔹 Step 2: Apply Values
\[ {}^{10}P_7 = \frac{10!}{3!} \]
—🔹 Step 3: Match with Options
\[ {}^{10}P_7 = {}^{10}C_7 \times 7! \]
—🔹 Final Answer
\[ \boxed{\text{Option (b)}} \]