[tex] \large\underline \bold{{SOLUTION}}[/tex]
Let n be the total of the cards and r be the times repeated cards are.
[tex]\longmapsto\rm{P_n= \frac{n!}{(r!)(r!)(r!)}}[/tex]
[tex]\longmapsto\rm{P_{10}= \frac{10!}{(5!)(2!)(3!)}}[/tex]
[tex]\longmapsto\rm{P_{10}= \frac{10×9×8×7×6×5×4×3×2×1}{(5×4×3×2×1)(2×1)(3×2×1)}}[/tex]
[tex]\longmapsto\rm{P_{10}= \frac{10×9×\cancel{8}^4×7×\cancel{6}×\cancel{5×4×3×2×1}}{(\cancel{5×4×3×2×1})(\cancel{2×1})(\cancel{3×2×1})}}[/tex]
[tex]\longmapsto\rm{P_{10}= 10×9×4×7}[/tex]
[tex]\longmapsto\boxed{\rm{P_{10}= 2520}}[/tex]
[tex] \large\underline{ \bold{ANSWER}}[/tex]
