<s>[INST] Probability of drawing a spade on the first draw, a heart on the second draw, and an ace on the third draw My answer is
$(\frac{1}{52})(\frac{1}{51})(\frac{2}{50})$ + $2(\frac{1}{52})(\frac{12}{51})(\frac{3}{50})$ + $(\frac{12}{52})(\frac{12}{51})(\frac{4}{50})$
= $\frac{1}{204}$
But the answer in the textbook is
$(\frac{13}{52})(\frac{13}{51})(\frac{2}{50})$ + $2(\frac{13}{52})(\frac{13}{51})(\frac{3}{50})$ + $(\frac{13}{52})(\frac{13}{51})(\frac{4}{50})$
= $\frac{13}{850}$
Which answer is correct?
 [/INST] The probability of drawing a spade followed by a heart followed by the ace of spades or hearts is
$$\frac{12\times13}{51\times 50}\times\frac2{52}.$$
The probability of drawing a spade followed by a heart followed by the ace of diamonds or clubs is is
$$\frac{13^2}{51\times 50}\times\frac2{52}.$$
These add to
$$\frac{13\times25}{51\times50}\times\frac2{52}=\frac1{204}.$$
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