Created trio

What is the probability that in the created trio, which consists of 19 boys and 12 girls, they will be:
a) the boys themselves
b) the girls themselves
c) 2 boys and 1 girl?

Correct answer:

p₁ =  21.5573 %
p₂ =  4.8943 %
p₃ =  45.6507 %

Step-by-step explanation:

$$\begin{gathered} c=19 \\ d=12 \\ s=c+d=19+12=31 \\ {p}_1=100\cdot {\displaystyle \frac{c\cdot (c-1)\cdot (c-2)}{s\cdot (s-1)\cdot (s-2)}}=100\cdot {\displaystyle \frac{19\cdot (19-1)\cdot (19-2)}{31\cdot (31-1)\cdot (31-2)}}=21.5573\mathrm{\%} \end{gathered}$$

$p_2=100\cdot {\displaystyle \frac{d\cdot (d-1)\cdot (d-2)}{s\cdot (s-1)\cdot (s-2)}}=100\cdot {\displaystyle \frac{12\cdot (12-1)\cdot (12-2)}{31\cdot (31-1)\cdot (31-2)}}={\displaystyle \frac{4400}{899}}\mathrm{\%}=4.8943\mathrm{\%}$

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