A standard 52-card deck contains four queens, twelve face cards, thirteen hearts (all red), thirteen diamonds (all red), thirteen spades (all black), and thirteen clubs (all black). Of the 752,538,150 different eight-card hands possible, decide how many would consist of the following. (a) all clubs (b) all black cards (c) all queens (a) There are 1287 ways to have a hand with all clubs. (Simplify your answer.) (b) There are $\square$ ways to have a hand with all black cards. (Simplify your answer.)

Step 1 ：A standard 52-card deck contains four queens, twelve face cards, thirteen hearts (all red), thirteen diamonds (all red), thirteen spades (all black), and thirteen clubs (all black). Of the 752,538,150 different eight-card hands possible, decide how many would consist of the following.

Step 2 ：(a) all clubs

Step 3 ：(b) all black cards

Step 4 ：(c) all queens

Step 5 ：For part (a), we need to choose 8 cards from the 13 clubs. This is a combination problem, and we can use the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and ! denotes factorial.

Step 6 ：For part (b), we need to choose 8 cards from the 26 black cards (13 spades and 13 clubs). This is also a combination problem, and we can use the same combination formula.

Step 7 ：Using the combination formula, we find that there are \(\boxed{1287}\) ways to have a hand with all clubs.

Step 8 ：Similarly, using the combination formula, we find that there are \(\boxed{1562275}\) ways to have a hand with all black cards.