Question 1039945
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For parts A) and B), I will be using the <a href="http://www.mathwords.com/c/combination_formula.htm">combination formula</a> since order does not matter.


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Part A)


Let's determine how many ways to pick 4 cards from a pool of 52.


n = 52
r = 4


n C r = (n!)/(r!(n-r)!)


52 C 4 = (52!)/(4!*(52-4)!)


52 C 4 = (52!)/(4!*48!)


52 C 4 = (52*51*50*49*48!)/(4!*48!)


52 C 4 = (52*51*50*49)/(4!) ... the <font color=blue>48!</font> terms cancel. 


52 C 4 = (52*51*50*49)/(4*3*2*1)


52 C 4 = (6497400)/(24)


52 C 4 = 270725


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Part B)


There are 26 black cards (spades and clubs). 


Let's determine how many ways to pick 4 cards from a pool of 26.


n = 26
r = 4


n C r = (n!)/(r!(n-r)!)


26 C 4 = (26!)/(4!*(26-4)!)


26 C 4 = (26!)/(4!*22!)


26 C 4 = (26*25*24*23*22!)/(4!*22!)


26 C 4 = (26*25*24*23)/(4!) ... the <font color=blue>22!</font> terms cancel. 


26 C 4 = (26*25*24*23)/(4*3*2*1)


26 C 4 = (358800)/(24)


26 C 4 = 14950


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Part C)


Divide the results of part B over part A


(result of part B)/(result of part A) = 14950/270725 = 0.05522208883553

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Summary:
Answer to part A: <font color=red>270725</font>
Answer to part B: <font color=red>14950</font>
Answer to part C: <font color=red>0.05522208883553</font>


Answer to part C is approximate. Make sure to round it however the book instructs. 
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