document.write( "Question 1144515: If I roll 5 regular dice out of a cup, what is
\n" ); document.write( "1. The probability that I will get 5 of a kind. I think the answer is 1 in 1296.
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Algebra.Com's Answer #765665 by Edwin McCravy(20064)\"\" \"About 
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1. The probability that I will get 5 of a kind.
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document.write( "There are 6 ways to succeed. They are to get 11111,22222,...,66666\r\n" );
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document.write( "Now we figure the number of ways they can land.\r\n" );
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document.write( "Imagine the 5 dice being labeled #1,#2,#3,#4,#5.\r\n" );
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document.write( "Die #1 can land any of 6 ways.\r\n" );
document.write( "Die #2 can land any of 6 ways\r\n" );
document.write( "Die #3 can land any of 6 ways.\r\n" );
document.write( "Die #4 can land any of 6 ways.\r\n" );
document.write( "Die #5 can land any of 6 ways.\r\n" );
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document.write( "That's 6 ways out of 6∙6∙6∙6∙6 = 7776 or 6/7776 = 1/1296\r\n" );
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document.write( "Another way to look at it is this:\r\n" );
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document.write( "Regardless of what number die A lands on,\r\n" );
document.write( "the probability that die B lands on that number is 1/6.\r\n" );
document.write( "the probability that die C lands on that number is 1/6.\r\n" );
document.write( "the probability that die D lands on that number is 1/6.\r\n" );
document.write( "the probability that die E lands on that number is 1/6.\r\n" );
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document.write( "(1/6)(1/6)(1/6)(1/6) = (1/6)(4 = 1/1296\r\n" );
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\n" ); document.write( "I think the answer is 1 in 1296.
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document.write( "You are right!\r\n" );
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\n" ); document.write( "2. What is the probability that I will get two pair, i.e., 22335, 55422, even
\n" ); document.write( "33433 would count as two pair.
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document.write( "Case 1. There are 4 the same and one with a different number. (like 33433)\r\n" );
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document.write( "Choose the number for there to be 4 of in 6 ways\r\n" );
document.write( "Choose the one number to be different in 5 ways.\r\n" );
document.write( "Choose the die to get the one different number in 5 ways.\r\n" );
document.write( "All the others can land on the other number in 1 way.\r\n" );
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document.write( "That's 6∙5∙5∙1 = 150 ways\r\n" );
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document.write( "Case 2. The two pairs are different numbers and one that's different from either\r\n" );
document.write( "(like 22335)\r\n" );
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document.write( "Choose the two numbers for the pairs in 6C2 = 15 ways.\r\n" );
document.write( "Choose the 2 dice to get the smaller of those two numbers in 5C2 = 10 ways.\r\n" );
document.write( "Choose the 2 of the 3 remaining dice as the pair to get the larger of those two\r\n" );
document.write( "numbers in 3C2 = 3 ways.\r\n" );
document.write( "Choose the 1 remaining die to get the single number in only 1 way.\r\n" );
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document.write( "That's 15∙10∙3∙1 = 450 ways.\r\n" );
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document.write( "Total number of successful ways = 150+450 = 600 ways\r\n" );
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document.write( "We have shown in the first problem that the total number of ways the 5 dice can\r\n" );
document.write( "land is 7776, so the desired probability is 600/7776 = 24/324.\r\n" );
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document.write( "Edwin
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