How many ways can you draw 5 cards with 3 from one suit and 2 from different suits?
Image: Marek Ślusarczyk (Tupungato) Photo portfolio, CC BY 3.0, via Wikimedia Commons
How many ways can you draw 5 cards with 3 from one suit and 2 from different suits?
Imagine you're at a party and want to play a card game that requires drawing 5 cards. You want to make sure you have 3 cards from the same suit and 2 cards from different suits.
Think of a standard deck of 52 cards, divided into 4 suits. You want 3 cards from one suit and 2 from the others. First, pick the suit for the 3 cards (4 choices), then choose 3 cards from that suit (12 ways), and finally pick 2 suits for the remaining cards (6 ways), and choose 1 card from each (4 ways for the first, 4 ways for the second).
Example
If you choose hearts for the 3 cards, there are 12 ways to pick those 3 hearts. Then, choose clubs and diamonds for the remaining 2 cards, which can be done in 6 ways (clubs and diamonds, diamonds and clubs), and then pick 1 card from each suit, which can be done in 4 ways for each suit.
Remember this
The total number of ways to draw 5 cards with 3 from one suit and 2 from different suits is 4 × 12 × 6 × 4 × 4.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
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