Question 170
In bridge, a standard 52-card deck is dealt in the usual way to 4 players. By convention, each hand is assigned a number of "points" based on the formula
$$
4 \times (\# \{ A \text{'s} \}) + 3 \times (\# \{ K \text{'s} \}) + 2 \times (\# \{ Q \text{'s} \}) + 1 \times (\# \{ J \text{'s} \})
$$
Given that a particular hand has exactly 4 cards that are A, K, Q, or J, find the probability that its point value is 13 or higher.
$$
4 \times (\# \{ A \text{'s} \}) + 3 \times (\# \{ K \text{'s} \}) + 2 \times (\# \{ Q \text{'s} \}) + 1 \times (\# \{ J \text{'s} \})
$$
Given that a particular hand has exactly 4 cards that are A, K, Q, or J, find the probability that its point value is 13 or higher.