3 cards are drawn at random from a pack of well shuffled 52 cards.find the probability that all the 3 cards are of the same suit.

Three cards are drawn at random from a pack of well shuffled $$52$$ cards. Find the probability that all the $$3$$ cards are of the same suit.

My two attempts:

1. $$\displaystyle\frac{ {13 \choose 3} }{ 52 } = \frac{ 11 }{ 850 }$$

2. $$\displaystyle\frac{ 13 \cdot 13 \cdot 13 }{52 \cdot 52 \cdot 52 } = \frac1{64}$$

Either way the answer is wrong as given in the book, which is $$\frac{22}{425}$$ .

What am I doing wrong?

• Why do you think the official answer is wrong? Hint: the first can be anything. The probability that the second has the same suit is then $\frac {12}{51}$. The probability that the third also matches is then... – lulu Dec 30 '18 at 12:24