eight cards are drawn from a standard deck of 52 cards. how many hands contain exactly 2 spades?
C(13,2) * C(39,5)
Me either
To calculate the number of hands that contain exactly 2 spades when drawing 8 cards from a standard deck of 52 cards, we can break down the problem into several steps.
Step 1: Determine the number of ways to choose 2 spades from the 13 spades in the deck. This can be calculated using the combination formula: C(13, 2) = 13! / (2! * (13 - 2)!), which equals 78.
Step 2: Determine the number of ways to choose the remaining 6 cards from the remaining 39 non-spades in the deck. This can be calculated using the combination formula: C(39, 6) = 39! / (6! * (39 - 6)!), which equals 3,262,623.
Step 3: Multiply the results from Steps 1 and 2 to obtain the total number of hands containing exactly 2 spades: 78 * 3,262,623 = 254,251,694.
Therefore, there are 254,251,694 possible hands that contain exactly 2 spades when drawing 8 cards from a standard deck of 52 cards.