Reiko takes 2 coins at random from the 3 quarters, 5 dimes, and 2 nickels in her pocket. three coins are tossed. what is the probability of 2 heads and 1 tail? what is the probability that she chooses a quarter followed by a dime?

The answers are 3/8 and 1/6.

There are 8 possible outcomes in the sample space for flipping 3 coins.  Of those, 3 include two heads and 1 tail.  This makes the probability 3/8.

Choosing a quarter for the first coin is 3/10, since there are 3 quarters out of 10 coins.  After this, choosing a dime is given by 5/9, since there are 5 dimes out of 9 coins left:
3/10(5/9) = 15/90 = 1/6