total ball 17
without replacement
rearagement 'ygbb' --> 4!/2! = 12
probability without rearagement
[tex] \frac{2}{17} \times \frac{5}{16} \times \frac{4}{15} \times \frac{3}{14} = \frac{1}{476} [/tex]
hence total probability
[tex] \frac{12}{476} = \frac{3}{119} [/tex]