# Boys and girls

There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?

Result

p =  27.094 %

#### Solution:

$n = 11+18 = 29 \ \\ \ \\ C_{{ 2}}(3) = \dbinom{ 3}{ 2} = \dfrac{ 3! }{ 2!(3-2)!} = \dfrac{ 3 } { 1 } = 3 \ \\ \ \\ p = 100 \cdot \ { { 3 } \choose 2 } \cdot \ \dfrac{ 11 }{ n } \cdot \ \dfrac{ 10 }{ n-1 } \cdot \ \dfrac{ 18 }{ n-2 } = 100 \cdot \ 3 \cdot \ \dfrac{ 11 }{ 29 } \cdot \ \dfrac{ 10 }{ 29-1 } \cdot \ \dfrac{ 18 }{ 29-2 } = \dfrac{ 5500 }{ 203 } \doteq 27.0936 = 27.094 \%$

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