[tex]\displaystyle\\|\Omega|=\binom{52}{13}=\dfrac{52!}{13!39!}=\dfrac{40\cdot41\cdot\ldots\cdot52}{2\cdot3\cdot\ldots\cdot13}=635013559600\\|A|=\binom{13}{4}\cdot\binom{13}{5}\cdot\binom{26}{4}=\dfrac{13!}{4!9!}\cdot\dfrac{13!}{5!8!}\cdot\dfrac{26!}{4!22!}=\dfrac{10\cdot11\cdot12\cdot13}{2\cdot3\cdot4}\cdot\dfrac{9\cdot10\cdot11\cdot12\cdot13}{2\cdot3\cdot4\cdot5}\cdot\\\cdot\dfrac{23\cdot24\cdot25\cdot26}{2\cdot3\cdot4}=13757064750\\\\P(A)=\dfrac{13757064750}{635013559600}=\dfrac{11962665}{552185704}[/tex]