Dice

We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?

Correct result:

p =  0.054

Solution:

q=1/6=160.1667 C4(10)=(104)=10!4!(104)!=109874321=210  p=(104) q4 (1q)6=210 0.16674 (10.1667)6=0.054q=1/6=\dfrac{ 1 }{ 6 } \doteq 0.1667 \ \\ C_{{ 4}}(10)=\dbinom{ 10}{ 4}=\dfrac{ 10! }{ 4!(10-4)!}=\dfrac{ 10 \cdot 9 \cdot 8 \cdot 7 } { 4 \cdot 3 \cdot 2 \cdot 1 }=210 \ \\ \ \\ p={ { 10 } \choose 4 } \cdot \ q^4 \cdot \ (1-q)^6=210 \cdot \ 0.1667^4 \cdot \ (1-0.1667)^6=0.054



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