Allen has 6 dimes, 4 nickels, and 2 pennies: in how many ways he can select 6 coins worth at least 50 cents

Answer 1

4 dimes and 2 nickles
10+10+10+10+5+5=50

Hope this helps!

Answer 2

start with the fewest coins possible to get exactly 50 cents. You can add any or all left-over nickels and pennies to each group of dimes and nickels
5d
Now start replacing the dimes with 2 nickels each
4d 2n
3d 4n