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A deck consists of 52 playing cards which is well shuffled. Draw 6 cards. Find the probability that among the cards there will be a representative of all suits?

can someone get to this answer  –-→   6283420/20358520

$P = \dfrac{{}^4C_1*{}^{13}C_3*13*13*13 +{}^4C_2*{}^{13}C_2*{}^{13}C_2*13*13}{{}^{52}C_{6}}$
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yeah, I got the same answer, which is $8682544/20358520$. On the back side of the textbook, it said that the answer is $6283420/20358520$, and I haven’t seen any mistakes in the answers at the back so far, which is why I’m a bit confused. I hope it’s just a mistake at the back.
i am also getting the same.