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Sagot :
Answer: [tex]\frac{16}{270725}[/tex]
This is the same as writing 16/270725
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Explanation:
There are 4 ways to draw a queen and 4 ways to select three kings (think of it like saying there are 4 ways to leave a king out). That produces 4*4 = 16 ways total to draw the four cards we want.
This is out of [tex]_{52}C_4 = 270,725[/tex] ways to select four cards without worrying if we got a queen and/or king. The steps to finding this number are shown below.
Divide the two values found to get the final answer [tex]\frac{16}{270725}[/tex]
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Scratch Work:
Computing the value of [tex]_{52}C_4[/tex]
Plug in n = 52 and r = 4 into the combination formula below
[tex]_{n} C _{r} = \frac{n!}{r!*(n-r)!}\\\\_{52} C _{4} = \frac{52!}{4!*(52-4)!}\\\\_{52} C _{4} = \frac{52*51*50*49*48!}{4!*48!}\\\\_{52} C _{4} = \frac{52*51*50*49}{4!} \ \ \text{ .... the 48! terms cancel}\\\\_{52} C _{4} = \frac{52*51*50*49}{4*3*2*1}\\\\_{52} C _{4} = \frac{6,497,400}{24}\\\\_{52} C _{4} = 270,725\\\\[/tex]
We use the nCr combination formula (instead of the nPr permutation formula) because order doesn't matter with card hands.
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