Your python code here! (Slow but functional.)
Reason:
- \( {9 \choose 2}\cdot 7 \) ways to choose digits for the pattern AABBC (first pick the digits to be A and B, then pick the digit to be C), then \( \frac{5!}{2!2!} \) distinct permutations from that pattern.
- \( {9 \choose 2}\cdot 7 \) ways to choose digits for the pattern AAABC (first pick the digits to be B and C, then pick the digit to be A), then \(\frac{5!}{3!}\) distinct permutations from that pattern.
Now \( {9 \choose 2} \cdot 7= \frac{9\cdot 8 \cdot 7}{2} = 252\) and \( \frac{5!}{2!2!}=5\cdot 3\cdot 2=30\) and \(\frac{5!}{3!}=5\cdot 4=20\).
So the total number is \( 252\cdot 30+252\cdot 20=252\cdot 50 = 12600\).