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What is the probability of obtaining exactly three "6" in 5 rolls of a fair dice?

 Jan 12, 2020
 #1
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The probability is 1/216.

 Jan 12, 2020
 #2
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You will need 3 6's and 2 not-6's.

The probability of getting a 6 is 1/6; the probability of getting a not-6 is 5/6.

(1/6)(1/6)(1/6)(5/6)(5/6)  =  25/7776.

You will need to multiply this answer by the number of ways that 3 6's can be chosen:  5C3 = 10.

Answer =  10 x 25 / 7776  =  0.0322  or  125/3888.

 Jan 13, 2020
 #3
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D=5; C=3; 5 nCr 3 * 5^(5 - 3) / 6^5 =3.21502057 % 

 Jan 13, 2020

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