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Combinations


How many different ways can a person draw 5 cards from a standard deck of cards without replacing them?



First, let's simplify the problem. How many ways can a person draw one card from a standard deck of cards?



Say we draw two cards from the deck. How many different ways can we do this? We know that there are 52 ways to draw the first card. So, let's pick it - say it is the ace of clubs.
Ace of Clubs ??? How many cards do you have left to pick from?
51


So, for every one of the 52 cards one could have picked first, there are 51 different cards left to pick from for your second choice. For example, say you picked the 4 of diamonds first. Then you have 51 different cards that you could have picked second:
4 of Diamonds
This table shows the 51 possible cards that may be chosen next


Since we could have done this with any of the 52 possible first choices, there are 52 * 51 = 2652 different ways to pick 2 cards from a deck of 52.

How many different ways do you suppose that we may draw 5 different cards from a deck?

Think about it, then click for the answer...






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