1
$\begingroup$

Is my solution correct?

There are two cases:

Case 1: (the chosen heart is not a king) So there are $3 \choose 1 $ ways to choose the king, and $12 \choose 1 $ ways to choose the heart, and then $52-12-3 \choose 3$ ways to choose rest of the three cards.

Case 2: (the chosen heart is a king) So there are $1 \choose 1$ way to choose the king (heart) card, and then since rest of the 4 cards cannot be a king nor heart, there are $52-1-12-3 \choose 4$ ways to choose the rest.

Then adding these two cases together we get the result.

$\endgroup$
1
$\begingroup$

Almost.

In the first case, once you select a king and a heart that is not the king of hearts, there are $16$ cards from which you cannot select the other three cards: the four kings and the hearts, as $13 + 4 - 1 = 16$. Therefore, you should have $$\binom{3}{1}\binom{12}{1}\binom{52 - 13 - 4 + 1}{3}$$

Your second case is fine.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.