document.write( "Question 1036516: i am really not sure how to go about this question ,i've tried it out using factorial but i still don't get it ,\r
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Algebra.Com's Answer #651192 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Obviously if there are 8 or more people or more \r\n" );
document.write( "in the room the probability is 1.\r\n" );
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document.write( "We go for the complement event, the event that n people \r\n" );
document.write( "all have different birth days.  Then subtract from 1.\r\n" );
document.write( "[Notice that \"birth day\" does not mean \"birthday\". LOL]\r\n" );
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document.write( "Case 1: One person in the room.  \r\n" );
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document.write( "The probability is 0 that 2 have the same birth day, for \r\n" );
document.write( "there aren't 2 people in the room.\r\n" );
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document.write( "Case 2: Two people in the room.\r\n" );
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document.write( "We can assign them all different birth days in 7P2 = 42 ways.\r\n" );
document.write( "We can assign them birthdays in 7*7=49 ways.  The \r\n" );
document.write( "probability that they have different birth days is \r\n" );
document.write( "42/49. So the probability that they have the same\r\n" );
document.write( "birthday 1-42/49 = 1/7 = 0.142871429\r\n" );
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document.write( "Case 3: Three people in the room.\r\n" );
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document.write( "We can assign them all different birth days in 7P3 = 210 ways.\r\n" );
document.write( "We can assign them birthdays in 7*7*7=343 ways.  The \r\n" );
document.write( "probability that they have different birth days is \r\n" );
document.write( "210/343. So the probability that they have the same\r\n" );
document.write( "birthday 1-210/343 = 19/49 = 0.387755102\r\n" );
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document.write( "Case 4: Four people in the room.\r\n" );
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document.write( "We can assign them all different birth days in 7P4 = 840 ways.\r\n" );
document.write( "We can assign them birthdays in 7*7*7*7=2401 ways.  The \r\n" );
document.write( "probability that they have different birth days is \r\n" );
document.write( "840/2401. So the probability that they have the same\r\n" );
document.write( "birthday 1-840/2401 = 223/343 = 0.6501457726\r\n" );
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document.write( "That's the answer, 4 people, but let's follow through\r\n" );
document.write( "for instructive purposes. \r\n" );
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document.write( "Case 5: Five people in the room.\r\n" );
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document.write( "We can assign them all different birth days in 7P5 = 2520 ways.\r\n" );
document.write( "We can assign them birthdays in 7*7*7*7*7=16807 ways.  The \r\n" );
document.write( "probability that they have different birth days is \r\n" );
document.write( "840/2401. So the probability that they have the same\r\n" );
document.write( "birthday 1-2520/16807 = 2041/2401 = 0.850062474\r\n" );
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document.write( "Case 6: Six people in the room.\r\n" );
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document.write( "We can assign them all different birth days in 7P6 = 5040 ways.\r\n" );
document.write( "We can assign them birthdays in 7*7*7*7*7*7=117649 ways.  The \r\n" );
document.write( "probability that they have different birth days is \r\n" );
document.write( "5040/117649. So the probability that they have the same\r\n" );
document.write( "birthday 1-5040/117649 = 112609/117649 = 0.9571607060\r\n" );
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document.write( "Case 7: Seven people in the room.\r\n" );
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document.write( "We can assign them all different birth days in 7P7 = 5040 ways.\r\n" );
document.write( "We can assign them birthdays in 7*7*7*7*7*7*7=823543 ways.  The \r\n" );
document.write( "probability that they have different birth days is \r\n" );
document.write( "5040/2401. So the probability that they have the same\r\n" );
document.write( "birthday 1-5040/823543 = 116929/117649 = 0.993880101\r\n" );
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document.write( "Edwin
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