Question 1140181: Classify the problem as a permutation, a combination, or neither.
In how many ways can two hearts be drawn from a deck of cards? (Order is not important.)
As well as answer the question.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! :
order is not important implies combination
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I will show you two methods for solving this problem
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Method 1 using combination and probability
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52C2 = 52!/(2! * (52-2)!) = 1326 ways to select 2 cards out of 52
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the probability(P) that the first card is a heart is 13/52 = 1/4
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the P that the second card is a heart is 12/51
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the P that both are hearts = 1/4 * 12/51 = 0.058823529
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multiply the P that both are hearts times the ways to select 2 cards out of 52
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0.058823529 * 1326 = 78 ways two hearts can be drawn from a deck of cards when order is not important
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Method 2 using selection process and combination
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13 * 12 = 156 ways to select two hearts
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since order is not important, we have to divide 156 by 2 - the reason for this is that there are 2 ways for each set of 2 hearts, for example, (4,5) and (5,4) were counted in the above calculation
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156/2 = 78 ways two hearts can be drawn from a deck of cards when order is not important
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