A fair die is rolled 6 times. What is the probability that t

Question

A fair die is rolled 6 times. What is the probability that the product of the numbers obtained is 6?

(A)  \frac{1}{6^6} 
(B)  \frac{1}{6^5} 
(C)  \frac{21}{6^6} 
(D)  \frac{5}{6^5} 
(E)  \frac{1}{6^4}

niks_1412 · Answer

Total number of cases = 6^6

Case 1:  5 times 1 and 1 time 6 
1,1,1,1,1,6
Total number of cases = 6!/5! = 6

Case 2:  4 times 1, 1 time 2 and 1 time 3
1,1,1,1,2,3
Total number of cases = 6!/4! = 30

Total number of times product is 6 = 6+30 = 36
Probability = 36/6^6 = 1/6^4

Answer is (E)

kevincan1 · Answer

Your second post was a good one!

uks7 · Answer

6! / 4! is not 6C4 . I guess those like me who chose C did exactly that.

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