# probability of card game bridge

In the card game bridge, each of 4 players is dealt a hand of 13 of the 52 cards.

1. What is the probability to get 13 cards that no one is Diamond?
2. What is the probability to get 13 cards that one suit is not appeared at all? I need to show it is 0.051.

thank you!

• In 2, what do you mean by shape? Do you mean suit? – user264781 Oct 28 '15 at 17:46
• yes! suit! @user264781 – user283468 Oct 28 '15 at 17:48
• For $(1)$, follow the hints in gt6989b's answer. For $(2)$, you need to use Inclusion exclusion principle, \begin{align} \verb/Prob/(\text{one suit is missing}) = & \binom{4}{1} \verb/Prob/(\text{one specific suit is missing}) \color{blue}{\leftarrow\text{ answer from }(1)}\\ - & \binom{4}{2} \verb/Prob/(\text{two specific suits are missing})\\ + & \binom{4}{3} \verb/Prob/(\text{three specific suits are missing}) \end{align} – achille hui Oct 28 '15 at 18:05

hints

• 1. $52\choose 13$ 2. $39\ \text{cards}$ 3. $39\choose 13$ 4. is for OP :) – user66407 Oct 28 '15 at 17:47