Home > CCA2 > Chapter 12 > Lesson 12.1.4 > Problem12-75

12-75.

From the $13$ spades in a deck of cards, four are selected. Find the probability that:

Use combinations to solve this problem.
For a review of Combinations see the Math Notes box in Lesson 10.1.1.

1. Exactly one card is a “face” card (Jack, Queen, or King).

There are $3$ face cards, choose $1$.
Then choose $3$ more cards for the $10$ that are not face cards.

$\frac{_3C_1\;·\;_{10}C_3}{_{13}C_4}=\frac{360}{715}$

2. The four cards can be rearranged to form a sequence $(\text{A},2,3,4;2,3,4,5; \ \ldots; \ \text{J, Q, K, A})$.

How many possible sequences of cards are there in the $13$ spades?
(Example: $A,2,3,4; 2,3,4,5;...; J,Q,K,A$)