To find the number of ways to select three coins from 5 dimes, 5 nickels, and 2 quarters such that the value of the coins is at least 25 cents, we need to consider all the possible combinations:
3 quarters
2 quarters and a nickel
2 quarters and a dime
1 quarter, 1 nickel, and 3 dimes
1 quarter, 2 nickels, and 2 dimes
3 nickels and 3 dimes
So, there are 6 possible ways to make the selection