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Precalculus

Lesson 5: Probability using combinatorics

Probability with permutations and combinations

Each card in a standard deck of 52 playing cards is unique and belongs to 1 of 4 suits:

Suppose that Luisa randomly draws 4 cards without replacement.

What is the probability that Luisa gets 2 diamonds and 2 hearts (in any order)?

(Choice A)
start fraction, 1, divided by, start subscript, 26, end subscript, start text, P, end text, start subscript, 4, end subscript, end fraction
(Choice B)
start fraction, 1, divided by, start subscript, 26, end subscript, start text, C, end text, start subscript, 4, end subscript, end fraction
(Choice C)
start fraction, start subscript, 13, end subscript, start text, C, end text, start subscript, 2, end subscript, divided by, start subscript, 52, end subscript, start text, C, end text, start subscript, 4, end subscript, end fraction
(Choice D)
start fraction, left parenthesis, start subscript, 13, end subscript, start text, C, end text, start subscript, 2, end subscript, right parenthesis, dot, left parenthesis, start subscript, 13, end subscript, start text, C, end text, start subscript, 2, end subscript, right parenthesis, divided by, start subscript, 52, end subscript, start text, C, end text, start subscript, 4, end subscript, end fraction

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