[tex] \large\underline \bold{{SOLUTION}}[/tex]
Let n be the total of the letters , and r be the times the repeated letters are.
[tex]\longmapsto\rm{P_n= \frac{n!}{(r!)(r!)(r!)(r!)(r!)(r!)(r!)}}[/tex]
[tex]\longmapsto\rm{P_9= \frac{9!}{(1!)(1!)(2!)(1!)(1!)(1!)(2!)}}[/tex]
[tex]\longmapsto\rm{P_9= \frac{9×8×7×6×5×4×3×2×1}{(1)(1)(2×1)(1)(1)(1)(2×1)}}[/tex]
[tex]\longmapsto\rm{P_9= \frac{9×8×7×6×5×\cancel{4}×3×2×1}{(\cancel{1)(1)(2×1)(1)(1)(1)(2×1})}}[/tex]
[tex]\longmapsto\rm{P_9=9×8×7×6×5×3×2}[/tex]
[tex]\longmapsto\boxed{\rm{P_9=90,720}}[/tex]
[tex] \large\underline{ \bold{ANSWER}}[/tex]
- 90 720 distinguishable permutations
