From a standard 52-card deck, how many 10-card hands contain all spades?
A hand of 10 spades can be chosen in $\square$ ways.
Answer
Final Answer: A hand of 10 spades can be chosen in \(\boxed{286}\) ways.
Step 1 ：We are given a standard 52-card deck, and we need to find out how many 10-card hands contain all spades.
Step 2 ：In a standard 52-card deck, there are 13 spades. We need to find out how many ways we can select 10 cards out of these 13.
Step 3 ：This is a combination problem which can be solved using the combination formula: \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to select, and ! denotes factorial.
Step 4 ：In this case, n = 13 (the total number of spades) and k = 10 (the number of spades to select).
Step 5 ：Substituting the values into the formula, we get \(C(13, 10) = \frac{13!}{10!(13-10)!} = 286\).
Step 6 ：Final Answer: A hand of 10 spades can be chosen in \(\boxed{286}\) ways.
