Firstly Picking a penny from a bag of 10 pennies, 14 nickels and 6 dimes gives a probability of
[tex]Probability=\frac{\#\text{ of required outcome}}{\text{sample space}}\frac{10}{10+14+6}=\frac{10}{30}=\frac{1}{3}[/tex]Next, picking a nickel out of 14 nickels, now 9 pennies and 6 dimes give a probability of
[tex]\frac{14}{9+14+6}=\frac{14}{29}[/tex]Lastly, picking a dime out of 6 dimes, now 9 pennies and 13 nickels give a probability of
[tex]\frac{6}{9+13+6}=\frac{6}{28}=\frac{3}{14}[/tex]Probability of having a penny, nickel and dime in that order is
[tex]\frac{1}{3}\times\frac{14}{29}\times\frac{3}{14}=\frac{1}{29}[/tex]