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Four cards are drawn one by one randomly without replacement from a pack of well shuffled 52 playing cards. The probability of getting at least one red card or at least one ace is $\frac{p}{q}$ , where p and q are coprime positive integers, then the number of positive factors of $(q - p) q$ is

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answer is 384.

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Detailed Solution

Required Probability
$= 1 - P$ (getting neither a red card nor an ace)
$= 1 - \frac{{}^{24}C_{4}}{{}^{52}C_{4}}$

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