# Families 2

There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys.

Result

n =  240

#### Solution:

$C_{{ 2}}(6) = \dbinom{ 6}{ 2} = \dfrac{ 6! }{ 2!(6-2)!} = \dfrac{ 6 \cdot 5 } { 2 \cdot 1 } = 15 \ \\ p={ { 2 } \choose 6 } \cdot \ (\dfrac{ 1 }{ 3 } )^{ 2 } \cdot \ (\dfrac{ 2 }{ 3 } )^{ 4 }=\dfrac{ 80 }{ 243 } \doteq 0.3292 \ \\ \ \\ n=729 \cdot \ p=729 \cdot \ 0.3292=240$

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