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A fair, six-sided die is rolled six times.  The six numbers are added up.  What is the probability that the sum of the six numbers is a multiple of 6?

 Dec 5, 2019

Best Answer 

 #1
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Expand (x + x^2 +x ^3 + x ^4 + x^5 + x^6)^6

 

x^36 + 6 x^35 + 21 x^34 + 56 x^33 + 126 x^32 + 252 x^31 + 456 x^30 + 756 x^29 + 1161 x^28 + 1666 x^27 + 2247 x^26 + 2856 x^25 + 3431 x^24 + 3906 x^23 + 4221 x^22 + 4332 x^21 + 4221 x^20 + 3906 x^19 + 3431 x^18 + 2856 x^17 + 2247 x^16 + 1666 x^15 + 1161 x^14 + 756 x^13 + 456 x^12 + 252 x^11 + 126 x^10 + 56 x^9 + 21 x^8 + 6 x^7 + x^6
 

Add up the coefficients of 6 + 12 + 18 + 24 + 30 + 36 =1 + 456 + 3431 + 3431 + 456 + 1 =7,776

The probability is: 7,776 / 6^6 = 1 / 6

 Dec 5, 2019
 #1
avatar
+1
Best Answer

Expand (x + x^2 +x ^3 + x ^4 + x^5 + x^6)^6

 

x^36 + 6 x^35 + 21 x^34 + 56 x^33 + 126 x^32 + 252 x^31 + 456 x^30 + 756 x^29 + 1161 x^28 + 1666 x^27 + 2247 x^26 + 2856 x^25 + 3431 x^24 + 3906 x^23 + 4221 x^22 + 4332 x^21 + 4221 x^20 + 3906 x^19 + 3431 x^18 + 2856 x^17 + 2247 x^16 + 1666 x^15 + 1161 x^14 + 756 x^13 + 456 x^12 + 252 x^11 + 126 x^10 + 56 x^9 + 21 x^8 + 6 x^7 + x^6
 

Add up the coefficients of 6 + 12 + 18 + 24 + 30 + 36 =1 + 456 + 3431 + 3431 + 456 + 1 =7,776

The probability is: 7,776 / 6^6 = 1 / 6

Guest Dec 5, 2019

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